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Complete Unit 4
Package
HighSchoolMathTeachers.com©2020
Table of Contents
Unit 4 Pacing Chart -------------------------------------------------------------------------------------------- 1
Geometry Unit 4 Skills List ---------------------------------------------------------------------------------------- 5
Unit 4 Lesson Plans -------------------------------------------------------------------------------------------- 6
Day 46 Bellringer -------------------------------------------------------------------------------------------- 33
Day 46 Activity -------------------------------------------------------------------------------------------- 36
Day 46 Practice -------------------------------------------------------------------------------------------- 38
Day 46 Exit Slip -------------------------------------------------------------------------------------------- 42
Day 47 Bellringer -------------------------------------------------------------------------------------------- 44
Day 47 Activity -------------------------------------------------------------------------------------------- 46
Day 47 Practice -------------------------------------------------------------------------------------------- 48
Day 47 Exit Slip -------------------------------------------------------------------------------------------- 54
Day 48 Bellringer -------------------------------------------------------------------------------------------- 56
Day 48 Activity -------------------------------------------------------------------------------------------- 58
Day 48 Practice -------------------------------------------------------------------------------------------- 61
Day 48 Exit Slip -------------------------------------------------------------------------------------------- 67
Day 49 Bellringer -------------------------------------------------------------------------------------------- 69
Day 49 Activity -------------------------------------------------------------------------------------------- 71
Day 49 Practice -------------------------------------------------------------------------------------------- 73
Day 49 Exit Slip -------------------------------------------------------------------------------------------- 78
Week 10 Assessment -------------------------------------------------------------------------------------------- 80
Day 51 Bellringer -------------------------------------------------------------------------------------------- 86
Day 51 Activity -------------------------------------------------------------------------------------------- 88
Day 51 Practice -------------------------------------------------------------------------------------------- 91
Day 51 Exit Slip -------------------------------------------------------------------------------------------- 96
Day 52 Bellringer -------------------------------------------------------------------------------------------- 98
Day 52 Activity -------------------------------------------------------------------------------------------- 101
Day 52 Practice -------------------------------------------------------------------------------------------- 104
Day 52 Exit Slip -------------------------------------------------------------------------------------------- 111
Day 53 Bellringer -------------------------------------------------------------------------------------------- 113
Day 53 Activity -------------------------------------------------------------------------------------------- 116
Day 53 Practice -------------------------------------------------------------------------------------------- 118
Day 53 Exit Slip -------------------------------------------------------------------------------------------- 120
Day 54 Bellringer -------------------------------------------------------------------------------------------- 123
Day 54 Activity -------------------------------------------------------------------------------------------- 125
Day 54 Practice -------------------------------------------------------------------------------------------- 129
Day 54 Exit Slip -------------------------------------------------------------------------------------------- 134
Week 11 Assessment -------------------------------------------------------------------------------------------- 136
Day 56 Bellringer -------------------------------------------------------------------------------------------- 145
Day 56 Activity -------------------------------------------------------------------------------------------- 147
Day 56 Practice -------------------------------------------------------------------------------------------- 149
Day 56 Exit Slip -------------------------------------------------------------------------------------------- 157
Day 57 Bellringer -------------------------------------------------------------------------------------------- 159
Day 57 Activity -------------------------------------------------------------------------------------------- 161
Day 57 Practice -------------------------------------------------------------------------------------------- 163
Day 57 Exit Slip -------------------------------------------------------------------------------------------- 167
Day 58 Bellringer -------------------------------------------------------------------------------------------- 169
Day 58 Activity -------------------------------------------------------------------------------------------- 172
Day 58 Practice -------------------------------------------------------------------------------------------- 174
Day 58 Exit Slip -------------------------------------------------------------------------------------------- 179
Day 59 Bellringer -------------------------------------------------------------------------------------------- 181
Day 59 Activity -------------------------------------------------------------------------------------------- 184
Day 59 Practice -------------------------------------------------------------------------------------------- 187
Day 59 Exit Slip -------------------------------------------------------------------------------------------- 195
Week 12 Assessment -------------------------------------------------------------------------------------------- 197
Day 61 Bellringer -------------------------------------------------------------------------------------------- 204
Day 61 Activity -------------------------------------------------------------------------------------------- 207
Day 61 Practice -------------------------------------------------------------------------------------------- 209
Day 61 Exit Slip -------------------------------------------------------------------------------------------- 215
Day 62 Bellringer -------------------------------------------------------------------------------------------- 217
Day 62 Activity -------------------------------------------------------------------------------------------- 219
Day 62 Practice -------------------------------------------------------------------------------------------- 222
Day 62 Exit Slip -------------------------------------------------------------------------------------------- 227
Day 63 Bellringer -------------------------------------------------------------------------------------------- 229
Day 63 Activity -------------------------------------------------------------------------------------------- 231
Day 63 Practice -------------------------------------------------------------------------------------------- 233
Day 63 Exit Slip -------------------------------------------------------------------------------------------- 237
Day 64 Bellringer -------------------------------------------------------------------------------------------- 239
Day 64 Activity -------------------------------------------------------------------------------------------- 242
Day 64 Practice -------------------------------------------------------------------------------------------- 244
Day 64 Exit Slip -------------------------------------------------------------------------------------------- 248
Unit 4 Test -------------------------------------------------------------------------------------------- 250
Unit 4 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 1
Unit Week Day CCSS Standards Objective I Can Statements
Unit 4 Triangle
Congruence
Week 10 – Transformat
ions to Theorems
46
CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to
transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use
the definition of congruence in terms of rigid motions to decide if they are congruent.
Come up with a result(conclusion) as a
result : Any rigid motion preserves
angle measure. Any rigid motion of the
plane is a reflection, rotation, translation or a
glide reflection. Any rigid motion maps straight segments to
straight segments, lines to lines, and circles to circles. An rigid motion maps any three non-collinear points into non-collinear points.
I can explain how and why: Any rigid motion preserves angle
measure. Any rigid motion of the plane is a reflection, rotation, translation or
a glide reflection. Any rigid motion maps straight segments to straight segments,
lines to lines, and circles to circles.
An rigid motion maps any three non-collinear points into non-
collinear points.
Unit 4 Triangle
Congruence
Week 10 – Transformat
ions to Theorems
47
CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to
transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use
the definition of congruence in terms of rigid motions to decide if they are congruent.
Come up with a result(conclusion) as a
result: Any plane rigid motion is
invertible. Any rigid motion with a
fixed point is either a reflection or a rotation
I can explain how and why: Any plane rigid motion is
invertible. Any rigid motion with a fixed
point is either a reflection or a rotation
Unit 4 Triangle
Congruence
Week 10 – Transformat
ions to Theorems
48
CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to
transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use
the definition of congruence in terms of rigid motions to decide if they are congruent.
Come up with a conclusion as a result:
The composition of two rigid motions is also a rigid
motion The composition of a half-turn and a reflection is a
glide reflection.
I can explain howand why: The composition of two rigid motions is also a rigid motion The composition of a half-turn
and a reflection is a glide reflection.
Unit 4 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 2
Unit 4 Triangle
Congruence
Week 10 – Transformat
ions to Theorems
49
CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to
transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use
the definition of congruence in terms of rigid motions to decide if they are congruent.
Come up with a conclusion as a result:
Successive reflection in two intersecting mirror lines
produces a rotation about the point of intersection through twice the angle
between the mirror lines. Successive reflection in
parallel mirror lines produces a translation in a direction perpendicular to
the mirrors through a distance equal to twice the
distance between the mirrors
Any rigid motion of the Euclidean plane can be
written as a composition of no more than 3 reflections.
I can explain how and why; Successive reflection in two
intersecting mirror lines produces a rotation about the point of
intersection through twice the angle between the mirror lines. Successive reflection in parallel
mirror lines produces a translation in a direction
perpendicular to the mirrors through a distance equal to twice the distance between the mirrors
and
Any rigid motion of the Euclidean
plane can be written as a composition of no more than 3
reflections.
Unit 4 Triangle
Congruence
Week 10 – Transformat
ions to Theorems
50 Assessment Assessment Assessment
Unit 4 Triangle
Congruence
Week 11 – Proofs of
Congruent Triangles
51
CCSS.MATH.CONTENT.HSG.CO.B.7 Use the definition of congruence in terms of rigid
motions to show that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
Identifying Congruent sides of a triangle
I can Identify congruent sides of a triangle
Unit 4 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 3
Unit 4 Triangle
Congruence
Week 11 – Proofs of
Congruent Triangles
52
CCSS.MATH.CONTENT.HSG.CO.B.7 Use the definition of congruence in terms of rigid
motions to show that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
Identifying Congruent angles of a triangle
I can Identifying congruent angles of a triangle
Unit 4 Triangle
Congruence
Week 11 – Proofs of
Congruent Triangles
53
CCSS.MATH.CONTENT.HSG.CO.B.7 Use the definition of congruence in terms of rigid
motions to show that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
Use the definition of congruence in terms of
rigid motions to show that two triangles are congruent if and only if corresponding
pairs of sides and corresponding pairs of angles are congruent.
I can use the definition of congruence in terms of rigid
motions to show that two triangles are congruent if and only if corresponding pairs of
sides and corresponding pairs of angles are congruent.
Unit 4 Triangle
Congruence
Week 11 – Proofs of
Congruent Triangles
54
CCSS.MATH.CONTENT.HSG.CO.B.7 Use the definition of congruence in terms of rigid
motions to show that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
Show Congruence of image and object distance in
dilation if scale factor is -1.
I can show congrence of image and object distance in dilation if
the scale factor is -1.
Unit 4 Triangle
Congruence
Week 11 – Proofs of
Congruent Triangles
55 Assessment Assessment Assessment
Unit 4 Triangle
Congruence
Week 12 – Congruent
Parts of Congruent Figures are Congruent
56
CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence
in terms of rigid motions.
Use the postulate SSS to show that triangles are
congruent. Also apply it so solve other geometric
problems.
I can use the postulate SSS to show that triangles are
congruent. I can apply the postulate so solve
other geometric problems.
Unit 4 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 4
Unit 4 Triangle
Congruence
Week 12 – Congruent
Parts of Congruent Figures are Congruent
57
CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence
in terms of rigid motions.
Use the postulate ASA to show that triangles are
congruent. Also apply it so solve other geometric
problems.
Use the postulate ASA to show that triangles are congruent. Also apply it so solve other geometric
problems.
Unit 4 Triangle
Congruence
Week 12 – Congruent
Parts of Congruent Figures are Congruent
58
CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence
in terms of rigid motions.
Use the postulate SAS to show that triangles are
congruent. Also apply it so solve other geometric
problems.
I can use the postulate SAS to show that triangles are
congruent. I can apply the postulate to solve
other geometric problems.
Unit 4 Triangle
Congruence
Week 12 – Congruent
Parts of Congruent Figures are Congruent
59
CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence
in terms of rigid motions.
Use the postulates SSS, SAS and ASA to show that triangles are congruent. Also apply them to solve
other geometric problems.
I can use the postulates SSS, SAS and ASA to show that triangles are congruent and also apply
them to solve other geometric problems.
Unit 4 Triangle
Congruence
Week 12 – Congruent
Parts of Congruent Figures are Congruent
60 Assessment Assessment Assessment
Geometry Unit 4 Skills List
HighSchoolMathTeachers.com©2020 Page 5
Geometry Unit 4 Skills List
Number Unit CCSS Skill
15 4 HSG.CO.B.6 Describing transformation theorems
16 4 HSG.CO.B.7 Showing congruence in triangles
17 4 HSG.CO.B.8 Explain the criteria for triangle
congruence
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 6
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 10 – Transformations to Theorems
Day: 46
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Mathematical Practice: Assessment
Objective: Come up with a result(conclusion) as a result : Any rigid motion preserves angle measure. Any rigid motion of the plane is a reflection, rotation, translation or a glide reflection. Any rigid motion maps straight segments to straight segments, lines to lines, and circles to circles. An rigid motion maps any three non-collinear points into non-collinear points.
I can statement: I can explain how and why: Any rigid motion preserves angle measure. Any rigid motion of the plane is a reflection, rotation, translation or a glide reflection. Any rigid motion maps straight segments to straight segments, lines to lines, and circles to circles. An rigid motion maps any three non-collinear points into non-collinear points.
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 7
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will reflect different shapes with a plane mirror and compare the geometric shape of the image with that of the object 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 46 Day 46 Activities Day 46 Practice Day 46 Presentation Day 46 Exit Slip
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 8
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 10 – Transformations to Theorems
Day: 47
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use apprpriate tools strategically. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
Objective: Come up with a result(conclusion) as a result: Any plane rigid motion is invertible. Any rigid motion with a fixed point is either a reflection or a rotation
I can statement: I can explain how and why: Any plane rigid motion is invertible. Any rigid motion with a fixed point is either a reflection or a rotation
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. They will illustrate the fixed points of an pre-images under rotation 3. The presentation will be used to look for misconceptions and encourage discussion.
Materials: Bellringer 47 Day 47 Activities Day 47 Practice Day 47 Presentation Day 47 Exit Slip
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 9
4. Students will complete the exit slip before leaving for the day.
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 10
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 10 – Transformations to Theorems
Day: 48
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use apprpriate tools strategically. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
Objective: Come up with a conclusion as a result: The composition of two rigid motions is also a rigid motion The composition of a half-turn and a reflection is a glide reflection.
I can statement: I can explain howand why: The composition of two rigid motions is also a rigid motion The composition of a half-turn and a reflection is a glide reflection.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of three to discover that the composition of two rigid motions is also a rigid motion
Materials: Bellringer 48 Day 48 Activities Day 48 Practice Day 48 Presentation Day 48 Exit Slip
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 11
3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 12
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 10 – Transformations to Theorems
Day: 49
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics. CCSS.MATH.PRACTICE.MP5 Use apprpriate tools strategically. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
Objective: Come up with a conclusion as a result: Successive reflection in two intersecting mirror lines produces a rotation about the point of intersection through twice the angle between the mirror lines. Successive reflection in parallel mirror lines produces a translation in a direction perpendicular to the mirrors through a distance equal to twice the distance between the mirrors Any rigid motion of the Euclidean plane can be written as a composition of no more than 3 reflections.
I can statement: I can explain how and why; Successive reflection in two intersecting mirror lines produces a rotation about the point of intersection through twice the angle between the mirror lines. Successive reflection in parallel mirror lines produces a translation in a direction perpendicular to the mirrors through a distance equal to twice the distance between the mirrors
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 13
and Any rigid motion of the Euclidean plane can be written as a composition of no more than 3 reflections.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 5. They will view image of an object between two parallel plane mirrors to discover their features 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 49 Day 49 Activities Day 49 Practice Day 49 Presentation Day 49 Exit Slip
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 14
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 10 – Transformations to Theorems
Day: 50
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 15
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 11 – Proofs of Congruent Triangles
Day: 51
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quatitatively.
Objective: Identifying Congruent sides of a triangle
I can statement: I can Identify congruent sides of a triangle
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 5 to illustrate the idea of congruent sides using rigid motions of a simply constructed triangle 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 51 Day 51 Activities Day 51 Practice Day 51 Presentation Day 51 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 16
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 17
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 11 – Proofs of Congruent Triangles
Day: 52
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quatitatively.
Objective: Identifying Congruent angles of a triangle
I can statement: I can Identifying congruent angles of a triangle
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of four to identify congruent angles in congruent triangles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 52 Day 52 Activities Day 52 Practice Day 52 Presentation Day 52 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 18
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 19
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 11 – Proofs of Congruent Triangles
Day: 53
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quatitatively. CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
Objective: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
I can statement: I can use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 5. They like show that if two triangles are congruent, then they have corresponding angles and sides. 3. The presentation will be used to look for misconceptions and encourage discussion.
Materials: Bellringer 53 Day 53 Activities Day 53 Practice Day 53 Presentation Day 53 Exit Slip
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 20
4. Students will complete the exit slip before leaving for the day.
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 21
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 11 – Proofs of Congruent Triangles
Day: 54
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Mathematical Practice: CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
Objective: Show Congrence of image and object distance in dilation if scale factor is -1.
I can statement: I can show congrence of image and object distance in dilation if the scale factor is -1.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will draw a triangle and its image under a dilation with a scale factor of -1 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 54 Day 54 Activities Day 54 Practice Day 54 Presentation Day 54 Exit Slip
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 22
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 23
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 11 – Proofs of Congruent Triangles
Day: 55
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 24
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 13 – Rigid Motion – Putting it all together
Day: 61
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quatitatively. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
Objective: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
I can statement: I can use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure Given two figures, I can use the definition of congruence in terms of rigid motions to decide if they are congruent.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will cut different triangles out of a rectangular plane paper and identify congruent and non congruent triangles
Materials: Bellringer 61 Day 61 Activities Day 61 Practice Day 61 Presentation Day 61 Exit Slip
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 25
3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 26
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 13 – Rigid Motion – Putting it all together
Day: 62
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quatitatively.
Objective: Identify Conguent angles and sides
I can statement: I can Identify Conguent angles and sides
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 2. They will learn how to identify congruent angles and sides using congruent triangles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 62 Day 62 Activities Day 62 Practice Day 62 Presentation Day 62 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 27
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 28
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 13 – Rigid Motion – Putting it all together
Day: 63
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quatitatively. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
Objective: Show that two triangles are or are not congruent using the biconditional statement in the standard
I can statement: I can show that two triangles are or are not congruent using the biconditional statement in the standard
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. Students will establish that if corresponding angles and sides of a triangle congruent, then the two triangles are congruent. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 63 Day 63 Activities Day 63 Practice Day 63 Presentation Day 63 Exit Slip
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 29
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 30
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 13 – Rigid Motion – Putting it all together
Day: 64
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quatitatively. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
Objective: Show that two triangles are or are not congruent using the postulates
I can statement: I can show that two triangles are or are not congruent using the postulates
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3.They will identify congruent triangles in a square that is divided into triangles by the diagonals 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 64 Day 64 Activities Day 64 Practice Day 64 Presentation Day 64 Exit Slip
Unit 4 Lesson Plan
HighSchoolMathTeachers.com©2020 Page 31
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Day 46 Bellringer
HighSchoolMathTeachers.com©2020 Page 32
Unit: Unit 4 Triangle Congruence
Course: Geometry
Topic: Week 13 – Rigid Motion – Putting it all together
Day: 65
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Day 46 Bellringer
HighSchoolMathTeachers.com©2020 Page 33
Identify the rigid motion involved in each of the following transformations.
a)
b)
c)
Day 46 Bellringer
HighSchoolMathTeachers.com©2020 Page 34
2. Which three rigid motions can be used to map the squares below?
3. The diagram below shows a square and a mirror line. Sketch the image of the square
Day 46 Bellringer
HighSchoolMathTeachers.com©2020 Page 35
Answer Key Day 46
1. a) Glide reflection
b) Translation
c) reflection
2. Reflection
Translation
Rotation
3.
Day 46 Activity
HighSchoolMathTeachers.com©2020 Page 36
1. Draw a line of 2 in on a plane paper.
2. Hold a plane mirror vertically and close to the line such that the image of the line is formed by the
plane mirror.
What is the geometric shape of the image?
3. Draw a circle of a convenient radius on a plane paper.
4. Hold the mirror vertically and close to the circle.
What is the geometric figure of the image?
5. Hold the mirror in different positions around the circle and observe whether shape of the image
changes.
Does the shape of the image change?
Day 46 Activity
HighSchoolMathTeachers.com©2020 Page 37
In this activity students will reflect different shapes with a plane mirror and compare the geometric
shape of the image with that of the object. Students will work in groups of at least three and each group
is required to have a plane mirror, a plane paper, a pencil, a ruler and a compass.
Answer Keys
Day 46:
1. No response
2. line
3. No response
4. Circle
5. No
Day 46 Practice
HighSchoolMathTeachers.com©2020 Page 38
Use the following information to answer questions 1 and 2.
A square of sides 6in by 6in was translated two units upwards and 3 units to the left.
1. What was the geometric figure of the image.
2. What was the area of the image.
Use the following information to answer questions 3 and 4.
A line of length 5 in is reflected through a line below it.
3. What is the shape of the image?
4. What is the length of the image?
In questions 5 to 12, State whether the given statement is true or false.
5. Rigid motions map a square to another smaller square.
6. A reflection maps a triangle to another triangle of the same size.
7. A rotation maps a right angle triangle to a scalene triangle.
8. A translation maps a square to a rectangle.
9. Any transformation that maps an object to an image of the same size and shape as the object is a rigid
motion.
10. A rotation can map non-collinear points to collinear points.
11. A reflection maps two intersecting lines into another two intersecting lines with different angle of
intersection.
12. Any rigid motion will map collinear points to collinear points.
Day 46 Practice
HighSchoolMathTeachers.com©2020 Page 39
Use the figure below to answer questions 13 – 15.
13. What is the value of ∝?
14. What is the value of 𝜃?
15. Find the value of 𝜑
67°
∝ 𝜃
𝜑
Day 46 Practice
HighSchoolMathTeachers.com©2020 Page 40
Use the figure below to answer questions 16 to 19. (figures are not drawn to scale)
16. Which rigid motion can map the two triangles?
17. What is the value of ∅?
18. What is the value of 𝜃?
19. What is the length of the side labelled y?
20. ∆𝐴𝐵𝐶 is reflected to map onto ∆𝐴′𝐵′𝐶′. If the side AB is 2 in long, What is the length of the side
𝐴′𝐵′ in the image.
44°
5in
y
∅
𝜃
Day 46 Practice
HighSchoolMathTeachers.com©2020 Page 41
Answer Keys Day 46:
1. square
2. 36𝑖𝑛2
3. Line
4. 5 𝑖𝑛
5. False
6. True
7. False
8. False
9. True
10. False
11. False
12. True
13. 67°
14. 67°
15. 46°
16. Translation
17. 44°
18. 46°
19. 5in
20. 2in
Day 46 Exit Slip
HighSchoolMathTeachers.com©2020 Page 42
1. A right triangle with sides 3 in, 4 in and 5 in is rotated in anti-clockwise through an angle of 90°. What
is the length of the longest side in the image.
Day 46 Exit Slip
HighSchoolMathTeachers.com©2020 Page 43
Answer Keys
Day 46:
1. 5 in
Day 47 Bellringer
HighSchoolMathTeachers.com©2020 Page 44
1. A triangle of area 15𝑠𝑞. 𝑖𝑛 is reflected twice about different mirror lines. Find the area of the final
image.
2. Explain your answer in 1 above.
3. A square of rotated through 3 full turns about the origin. What would be the interior angles of the
final image?
4. Explain your answer in 3 above.
5. Draw the image of the following lines after reflection about the given mirror line.
Day 47 Bellringer
HighSchoolMathTeachers.com©2020 Page 45
Answer Key
Day 47
1. 15 𝑠𝑞. 𝑖𝑛
2. The size of the triangle does not change under reflection(s)
3. All angles are 90°
4. The shape, consequently, the angle measure of a figure does not change due to rotation(s).
5.
Day 47 Activity
HighSchoolMathTeachers.com©2020 Page 46
1. Mount the plane paper on the softwood using the masking tape.
2. Place the plastic bar on the peace of paper and draw its pre-image by making a line along its
boundaries.
3. Select any point on the bar and drive the pushpin so that it holds the bar against the paper on the
softwood.
4. Using one of your fingers, push one side (unmounted side) of the bar so that it rotates due to the
force.
5. Stop when the bar makes a rotation between 90° and 180°.
6. Trace the image of the bar at that particular point and label it the pre-image. Remove the bar and the
pin from the plane paper.
7. Which direction of rotation did you take?
8. Which angle did the bar rotate, positive or negative?
9. Identify the name given to the position of the pin in relation to the motion of the bar.
10. By keenly looking at the image and its pre-image, which point did not move?
11. Can you make a conclusion about fixed points in relation to the motion of the bar?
Day 47 Activity
HighSchoolMathTeachers.com©2020 Page 47
In this activity, we would like to illustrate the fixed points of an pre-images under rotation. Each group is
required to have a pushpin, a thin plastic short bar (about 3 in – 4 in) or a thin wooden bar that can be
placed through by the pushpin, a plane A4 paper, masking tape, softwood and a pencil.
Answer Keys
Day 47:
1 – 6.No response
7. Difference responses; clockwise or counterclockwise
8. If clockwise the answer should be negative and if counterclockwise the answer is positive
9. Center of rotation
10. Point at the position of the pin
11. In rotation, the points of the pre-image that is also the center of rotation remains fixed after rotation
of any angle.
Day 47 Practice
HighSchoolMathTeachers.com©2020 Page 48
Use the following information to answer questions 1 - 10.
In each of the following identify the transformation that will map the image back to the pre image given
the pre-image and the initial transformation.
1. Image of a reflection of a triangle along its smallest side.
2. Image of a reflection of a rectangle about one of its diagonal.
3. Image after a rotation of 60° about the origin.
4. Image after translation of vector (2
−5).
5. Image after translation of vector (−3−1
).
6. Imge after rotating a pentagon through a negative quarter turn about (1,0).
7. Image after translating an object 5 units upwards and 3 units to the right.
8. Image after rotating a triangle 187° in the counterclockwise direction.
9. Image after reflection an equilateral triangle about 𝑥 = −3.
10. Image of a unit square after reflecting it about 𝑦 + 𝑥 = 0.
Use the following statement to answer questions 11 – 17.
Identify the fixed points of the pre-image after the following motion
11. Reflection about line M
M
Day 47 Practice
HighSchoolMathTeachers.com©2020 Page 49
12. Rotation about O.
13. 360° rotation of a unit circle about point (−5,7).
14. Reflection of a right triangle along its hypotenuse.
15. The following translation
16.
O
A
B
C
E
C’
D’ A’
B’
D E’
P Q
R
𝑇
𝑉
Day 47 Practice
HighSchoolMathTeachers.com©2020 Page 50
17.
Use the following information to answer questions 18 – 20.
Find the pre-image given the following images after the transformations given.
18. Reflection about the vertical line
M
V
P
Q
L
Day 47 Practice
HighSchoolMathTeachers.com©2020 Page 51
19. Rotated through a negative quarter turn about the center.
20. Translated 3 units up and 1 unit to the right
Day 47 Practice
HighSchoolMathTeachers.com©2020 Page 52
Answer Keys
Day 47
1. Reflect the image about the same smallest side
2. Reflect the rectangle about the same diagonal
3. Rotate the image through −60° about the origin
4. Translate the image through vector (−25
).
5. Translate the image through vector (31
).
6. Rotate the image (the pentagon) through positive quarter turn about (1,0).
7. Translate the object 5 units downwards and 3 units to the left.
8. Rotate the triangle through −187° .
9. Reflect the equilateral triangle about 𝑥 = −3.
10. Reflect the unit square about 𝑦 + 𝑥 = 0.
11. Points on the pre-image that lies on line M
12. Point Q
13. All points on the circle
14. Points along the hypotenuse
15. None
16. Point Q
17. Points along line PQ
18.
19.
Day 47 Practice
HighSchoolMathTeachers.com©2020 Page 53
20.
Day 47 Exit Slip
HighSchoolMathTeachers.com©2020 Page 54
Identify the fixed point(s) of rectangle rotated about 180° about a point that lies on one of its diagonal.
Day 47 Exit Slip
HighSchoolMathTeachers.com©2020 Page 55
Answer Keys
Day 47
The fixed point is the center of rotation which is a point on one of its diagonals
Day 48 Bellringer
HighSchoolMathTeachers.com©2020 Page 56
1. (a) List any three types of rigid motions of the plane you have learnt in class.
(b) What happens to the shape of the pre-image after undergoing a given rigid motion?
(c) What happens to the size of the pre-image after undergoing a given rigid motion?
(d) What happens to the angle measures of the pre-image after undergoing a given rigid motion to form
the corresponding image?
2. (a) If a rectangle is rotated about a given point along the coordinate plane, then the image further
reflected about a given line of reflection, what happens to its shape and size after the two transformations?
(b) The figure below represents a pre-image and its corresponding image after a transformation.
Is this kind of transformation a rigid motion or not? Give a reason to support your answer.
Pre-image
Image
Day 48 Bellringer
HighSchoolMathTeachers.com©2020 Page 57
Answer Keys
Day 48:
1. (a) Rotations, reflections, translations and glide reflections.
(b) The shape remains unchanged/ it is preserved
(c) The size remains unaltered/ it is preserved
(d) Angle measure is preserved
2. (a) The size and shape are both preserved after the rigid motions
(b) It is not a rigid motion, though the shape is preserved, the size has changed after the
transformation.
Day 48 Activity
HighSchoolMathTeachers.com©2020 Page 58
1. Draw the coordinate plane on the grid using a ruler labelling the x-axis and the y-axis as shown below.
2. On the grid, draw triangle PQR in the position as shown below. This is the pre-image.
Day 48 Activity
HighSchoolMathTeachers.com©2020 Page 59
3. Translate the triangle through (𝑥 + 2, 𝑦) to its image along the coordinate plane and label it P′Q′R′.
4. Examine the two triangles, measure their corresponding lengths using a ruler and their corresponding
angles using a protractor. What does this tell you about their shape and size?
5. Now, using triangle P′Q′R′ as your pre-image reflect it along the x-axis and label the resulting image
P′′Q′′R′′.
6. Consider triangles P′Q′R′ and P′′Q′′R′′. Measure their corresponding lengths using a ruler and their
corresponding angles using a protractor. What does this tell you about their shape and size?
7. Consider triangles PQR and P′′Q′′R′′. Measure their corresponding lengths using a ruler and their
corresponding angles using a protractor. What does this tell you about the shape and size?
8. What do you conclude about the three triangles after performing the two transformations? Base your
conclusion on the responses you have given in questions 6 and 7.
Day 48 Activity
HighSchoolMathTeachers.com©2020 Page 60
In this activity students will work in groups of three to discover that the composition of two rigid
motions is also a rigid motion. The students in the respective groups will require a graph paper (grid), a
ruler and a protractor.
Answer Keys Day 48:
1. No response
2. No response
3. No response
4. They have the same size and shape/ They are congruent
5. No response
6. They have the same size and shape/ They are congruent
7. They have the same size and shape/ They are congruent
8. All the three triangles are congruent/ Shape and size is preserved.
Day 48 Practice
HighSchoolMathTeachers.com©2020 Page 61
Study the diagram below and use it to answer questions 1- 8.
1. What type of transformation maps Δ ABC onto Δ A′B′C′?
2. What type of transformation maps Δ A′B′C′ onto Δ A′′B′′C′′?
3. Considering Δ ABC and Δ A′′B′′C′′ show the mapping of corresponding line segments in the two
triangles.
4. Considering Δ ABC and Δ A′′B′′C′′ show the mapping of corresponding angles in the two triangles.
5. Basing on questions 3 and 4 above, what do you say about Δ ABC and Δ A′′B′′C′′?
6. Identify one type of rigid motion that maps Δ ABC and Δ A′′B′′C′′.
A
B C
B′ C′
A′
B′′ C′′
A′′
Mirror line, l
Day 48 Practice
HighSchoolMathTeachers.com©2020 Page 62
7. Considering the two types of rigid motions shown above, does Δ ABC change its shape and size after
being transformed onto the final image Δ A′′B′′C′′?
8. According to question 7 above, what is your conclusion about the composition of two rigid motions?
The diagram below shows a sequence of two rigid motions that map rectangle WXYZ onto the final
image. Study it and use it to answer questions 9-14.
9. What type of rigid motion maps rectangle WXYZ onto rectangle W′X′Y′Z′?
10. What type of rigid motion maps rectangle W′X′Y′Z′ onto W′′X′′Y′′Z′′?
11. Considering rectangle WXYZ and rectangle W′′X′′Y′′Z′′ show the mapping of corresponding sides.
12. Considering rectangle WXYZ and rectangle W′′X′′Y′′Z′′ show the mapping of corresponding angles.
13. How are the sizes of rectangles WXYZ and W′′X′′Y′′Z′′ related basing on questions 11 and 12 above?
Day 48 Practice
HighSchoolMathTeachers.com©2020 Page 63
14. Considering the two transformations and the sizes and shapes of the three rectangles, what do you
discover?
The grid below shows a composition of two rigid motions, study it then answer questions 15-20.
15. Give that ΔPQR is mapped onto ΔP′Q′R′ through a rotation of 180° about the point (0,0), what type
of rigid motion maps Δ P′Q′R′ onto Δ P′′Q′′R′′?
Day 48 Practice
HighSchoolMathTeachers.com©2020 Page 64
16. On the grid draw the image of Δ P′′Q′′R′′ using dotted lines after a reflection along the x-axis.
17. What type of rigid transformation is supposed to map the dotted triangle you have drawn in 16
above to ΔPQR?
18. Considering ΔPQR, the dotted triangle and Δ P′′Q′′R′′. Which single rigid motion will map
Δ P′′Q′′R′′onto ΔPQR?
19. Considering the type of transformation you have identified in question 18 above, what do you notice
about relationship between the shape and size of ΔPQR and ΔP′′Q′′R′′?
20. Considering the two sequences of transformations listed below, what do you deduce?
Sequence 1: ΔPQR → ΔP′Q′R′ → Δ P′′Q′′R′′
Sequence 2: ΔP′′Q′′R′′ → dotted triangle → Δ PQR
P
Q
y
x
R
−6 − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 6 7
5
4
3
2
1
−1
−2
P′
Q′ R′ Q′′ R′′
P′′
Day 48 Practice
HighSchoolMathTeachers.com©2020 Page 65
Answer keys
Day 48:
1. Reflection
2. Translation
3. AB → A′′B′′; BC → B′′C′′; CD → C′′D′′
4. ∠A → ∠A′′, ∠B → ∠B′′, ∠C → ∠C′′
5. ABCD ≅ A′′B′′C′′D′′
6. Glide reflection
7. No
8. The composition of two rigid motions is also a rigid motion
9. Reflection
10. Rotation
11. WX → W′′X′′; XY → X′′Y′′; YZ → Y′′Z′′ and WZ → W′′Z′′
12. ∠W → ∠W′′, ∠X → ∠X′′, ∠Y → ∠Y′′and ∠Z → ∠Z′′
13. WXYZ ≅ W′′X′′Y′′Z′′
14. A sequence of two rigid motions is still a rigid motion, distances and angle measures are preserved.
15. Reflection
Day 48 Practice
HighSchoolMathTeachers.com©2020 Page 66
16.
17. Translation
18. Glide reflection
19. ΔPQR ≅ Δ P′′Q′′R′′
20. The two sequences of rigid motions are the same. The composition of a half-turn and a reflection is
just a glide reflection.
P
Q
y
x
R
−6 − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 6 7
5
4
3
2
1
−1
P′
Q′ R′ Q′′ R′′
P′′
Day 48 Exit Slip
HighSchoolMathTeachers.com©2020 Page 67
The grid below shows a composition of two rigid motions, a half turn about the origin (0,0) followed by
a reflection along the line 𝑥 = 1 performed on a square PQRS.
(a) On the grid draw the image of square P′′Q′′R′′S′′ using dotted lines after a reflection along the x-axis.
(b) What type of transformation will map the dotted square you have drawn in (a) above to square
PQRS?
(c) Consider square PQRS, the dotted square and square P′′Q′′R′′S′′. What single transformation will
map square P′′Q′′R′′S′′ onto square PQRS?
(d) Given that square PQRS has been transformed through a half turn about the origin (0,0) followed by
a reflection along the line 𝑥 = 1, relate this transformation to the transformation described in (c) above.
What do you notice?
P
Q
y
x
R
S
−6 − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 6 7
5
4
3
2
1
−1
−2
P′
Q′
S′
R′ Q′′ R′′
P′′ S′′
Day 48 Exit Slip
HighSchoolMathTeachers.com©2020 Page 68
Answer Keys Day 48:
(a)
(b) A translation
(c) A glide reflection
(d) The composition of a half-turn and a reflection is a glide reflection.
P
Q
y
x
R
S
−6 − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 6 7
5
4
3
2
1
−1
−2
P′
Q′
S′
R′ Q′′ R′′
P′′ S′′
Day 49 Bellringer
HighSchoolMathTeachers.com©2020 Page 69
1. Use the graph below to answer the questions that follow
a) If ∆𝐴𝐵𝐶 is rotated −180° about the origin, what will be the new coordinates of point C?
b) Indicate the image on the graph above, if ∆𝐴𝐵𝐶 is translated 5 units upwards along y-axis.
c) What will the new coordinates of point B if ∆𝐴𝐵𝐶 is reflected over the line 𝑥 = 1?
d) What will be the new coordinates of point B if ∆𝐴𝐵𝐶 is reflected over the x-axis?
2. The triangle below is reflected over the given mirror line. Draw the image.
Day 49 Bellringer
HighSchoolMathTeachers.com©2020 Page 70
Answer Key
Day 4
1 a) (1,1)
b)
c) (3, −4)
d) (−1,4)
2.
Day 49 Activity
HighSchoolMathTeachers.com©2020 Page 71
1. Draw two parallel lines 6 inches apart on a plane paper and label them 𝐿1 and 𝐿2.
2. Write the letter ‘K’ in between the lines as shown.
3. Hold the plane mirror vertically on 𝐿1 and view the letter ‘K’.
Does it have the same orientation as the original letter?
4. Hold the plane mirror vertically on 𝐿2 and view the letter ‘K’.
Does it have the same orientation as the original letter?
5. Position the plane mirrors vertically on both lines and observe the images of letter ‘K’.
6. Observe the second image from each plane mirror.
Does it appear like a translation of the letter ‘K’?
K
𝐿1 𝐿2
Day 49 Activity
HighSchoolMathTeachers.com©2020 Page 72
In this activity students will view image of an object between two parallel plane mirrors.
Students will work in groups of at least 5 and each group is required to have two plane mirrors, a plane
paper and a pen.
Answer Keys
Day 49:
1-2. No response
3. No
4. No
5. No response
6. Yes
Day 49 Practice
HighSchoolMathTeachers.com©2020 Page 73
A square measuring 1in by 1in was placed between two plane mirrors 2 inches apart as shown. Use this
diagram to answer questions 1-5.
1. What is least distance we can translate the square to the left such that it coincides with its image
resulting from two successive reflection of the two mirrors?
2. What will be the distance between the image of the square and 𝑀1 if the square is translated to the
left until it coincides with the image resulting from successive reflection of the two mirrors?
3. What will be the distance between the image of the square and 𝑀2 if the square is translated to the
left until it coincides with the image resulting from successive reflection of the two mirrors?
4. What will be the distance between the image of the square and 𝑀2 if the square is translated to the
right until it coincides with the image resulting from successive reflection of the two mirrors?
5. What will be the distance between the image of the square and 𝑀1 if the square is translated to the
right until it coincides with the image resulting from successive reflection of the two mirrors?
Use the information below to answer questions 6 and 7.
A circle centered at the origin is drawn in 𝑥𝑦 plane such that two parallel and vertical mirror lines makes
a tangent with it. One of the mirror lines is the line 𝑥 = −1.
6. What will be the coordinates the center of circle if it is translated to the left until it coincides with the
image resulting from two successive reflections of the two mirror lines?
𝑀1 𝑀2
Day 49 Practice
HighSchoolMathTeachers.com©2020 Page 74
7. What will be the coordinates the center of circle if it is translated to the right until it coincides with
the image resulting from two successive reflections of the two mirror lines?
Two mirror lines at the lines 𝑦 = −𝑥 + 3 and 𝑦 = 𝑥 + 1 successively reflects a square with its vertex at
point V(1,1). Use this iformation to answer questions 8 and 9.
8. If these reflections are described by a rotation, what will be the coordinates of the center of rotation?
9. If these reflections are described by a rotation, what will be the angle of rotation?
Day 49 Practice
HighSchoolMathTeachers.com©2020 Page 75
Use the graph below to answer questions 10-13.
10. Describe a single rigid motion which can map ∆𝐴𝐵𝐶 to its image.
11. Identify to mirror lines which can successively map ∆𝐴𝐵𝐶 to its image.
12. ∆𝐴𝐵𝐶 is successively reflected by two mirror lines at 𝑥 = −1 and 𝑥 = −4. On the graph, indicate the
image of ∆𝐴𝐵𝐶 to its left that results from two successive reflections of the two mirrors.
13. Describe a translation which can descried the series of reflections in NO. 12.
14. A student was passing through the center of a square room with vertical plane mirrors on opposite
sides of the wall. The room was measuring 10ft by 10ft. He noticed that multiple images were formed.
How far from the student was the image which could appear exactly as a translation.
-6 -4 -2 0 2 4 6 x
y
4
2
-2
-4
A B
C
𝐶′
𝐵′ 𝐴′
Day 49 Practice
HighSchoolMathTeachers.com©2020 Page 76
15. A barber fitted plane mirrors on two adjacent walls of his square barber shop. As he stood at the
center of his shop he noticed that there were three images of his body formed by the plane mirrors.
Which single rigid motion could map his body with the central image?
Use the following information to answer questions 16,17 and 18.
An hotelkeeper fitted his rectangular hotel with vertical plane mirrors on opposite walls. The distance
between the two opposite walls was 12ft. He then placed a table at the center of the hotel and noticed
that multiple images of the table formed on the plane mirrors. Two images with the same orientation as
the original table formed on both sides of the wall.
16. How long was the distance between the table and one image which had the same orientation as the
table.
17. What was the shortest distance between the two images which had the same orientation as the
table.
18. How far was one of the images from the wall.
In questions 19 and 20 state whether the given statement is true or false.
19. Any rotation can be written as two successive reflections.
20. A rotation of 45° about the origin can be described by two successive reflections with mirrors lines
intersected at the origin and making an angle of 90° with each other.
Day 49 Practice
HighSchoolMathTeachers.com©2020 Page 77
Answer Keys Day 49:
1. 4𝑖𝑛
2. 3𝑖𝑛
3. 5in
4. 2𝑖𝑛
5. 4𝑖𝑛
6. (−4,0)
7. (4,0)
8. (1,2)
9. 180°
10. A rotation of 180° about the point (0,1)
11. 𝑥 = 0, 𝑦 = 1
12.
-6 -4 -2 0 2 4 6 x
y
4
2
-2
-4
A B
C
𝐶′
𝐵′ 𝐴′
Day 49 Exit Slip
HighSchoolMathTeachers.com©2020 Page 78
1. In the graph below, ∆𝐴𝐵𝐶 is mapped onto ∆𝐴′𝐵′𝐶′ by a rotation of 180° about the point (0,1). Write
the equation of two mirror lines which can describe the transformation.
-6 -4 -2 0 2 4 6 x
y
4
2
-2
-4
A
B C
𝐴′
𝐶′ 𝐵′
Day 49 Exit Slip
HighSchoolMathTeachers.com©2020 Page 79
Answer Keys
Day 49:
1. 𝑦 = 1
𝑥 = 0
80
High School Math Teachers
Geometry
Weekly Assessment Package
Week 10
©2020HighSchoolMathTeachers
81
Week 10
Weekly Assessments
82
Week #10 1. Construct an equilateral triangle inscribed in a circle of radius 1 in.
2. Construct a square inscribed in a circle of diameter 2.5 in
3. Construct a regular hexagon inscribed in a circle of radius 1.2 in
4. a. Identify four rigid motions
b. Identify those that preserves orientations and those that do not. c. Identify those that have fixed point(s) and those that do not.
5. An geometric figure is reflected about
𝑦 = 𝑥 then rotated by 90°about (1,2).
a. Compare the sizes of the two
images
b. Comment on the orientation of
the two images
c. Compare the interior angles of
the images.
6. Identify all fixed point on the figure
ABCD id reflected about line M.
B
A
C
D E
M
83
Week 10 - Keys
Weekly Assessments
84
Week #10 KEY 1. Construct an equilateral triangle inscribed in a circle of radius 1 in.
2. Construct a square inscribed in a circle of diameter 2.5 in
3. Construct a regular hexagon inscribed in a circle of radius 1.2 in 0722 486064/0723
003357
85
4. a. Identify four rigid motions
Rotation Translation Refection Glide reflection b. Identify those that preserves orientations and those that do not. Translation c. Identify those that have fixed point(s) and those that do not. Rotation Reflection Glide reflection
5. An geometric figure is reflected about
𝑦 = 𝑥 then rotated by 90°about (1,2).
a. Compare the sizes of the two
images
They have the same size
b. Comment on the orientation of
the two images
They have different orientations
c. Compare the interior angles of
the images.
The corresponding angles are equal
6. Identify all fixed point on the figure
ABCD id reflected about line M.
Fixed points are points that will not move after the transformation. These are all points on ABCD that lie on M.
B
A
C
D E
M
Day 51 Bellringer
HighSchoolMathTeachers.com©2020 Page 86
1. Identify rigid motions that preserves the orientation of the pre image
2. Identify rigid motions that do not preserves the orientation of the pre image.
3. Why is dilation not a rigid motion?
4. How can you describe parallel lines
5. What is common about corresponding angles of parallel line?
Day 51 Bellringer
HighSchoolMathTeachers.com©2020 Page 87
Answer Key
Day 51
1. Translation
2. Rotation, reflection and glide reflection
3. Because it involves change in size of the pre-image hence not qualifying to be a rigid motion
where sizes does not change
4. They are lines in the same plane that do not meet, they maintain the same distance along
their length
5. They face in the same direction and they are equal.
Day 51 Activity
HighSchoolMathTeachers.com©2020 Page 88
1. Using the rubber bands, tied the three bars to form a triangle.
2. Place the triangle on the ground and draw its image, label it. ABC.
3. Take it and drop it to the ground with any angle or side facing any direction. Draw its image then
label it DEF. In each case, not the side with the same color and the initial one.
4. Take it and drop it to the ground with any angle or side facing any direction. Draw its image then label
it GHI. In each case, not the side with the same color and the initial one.
4. Take it and drop it to the ground with any angle or side facing any direction. Draw its image then label
it JKL. In each case, not the side with the same color and the initial one.
5. Take it and drop it to the ground with any angle or side facing any direction. Draw its image then label
it MNP. In each case, not the side with the same color and the initial one.
6. Take it and drop it to the ground with any angle or side facing any direction. Draw its image then label
it QRS. In each case, not the side with the same color and the initial one.
7. Proceed with the similar procedure until you get as much triangle labels as possible.
Day 51 Activity
HighSchoolMathTeachers.com©2020 Page 89
8. List all sides with the same color.
9. A part from color, Identify any geometrical features that the sides with the same colour have?
10. What is the best name to describe the solution in 9 above.
Day 51 Activity
HighSchoolMathTeachers.com©2020 Page 90
In this activity, we would like to illustrate the idea of congruent sides using rigid motions of a simply
constructed triangle. Students will work in groups of at least 5. Each group is required to have three
plastic thin bars of any size between 2 in and 10 in (or any thin bar that can be identified to be different)
rubber bands and an open field where we can scribble down or any field together with whitewash to
make us make drawings.
Answer Keys
Day 51:
1 – 2.No response
3 -7. Different responses
7. Difference responses
8. They should be in 3 different groups
9. They are equal
10. Congruent sides
Day 51 Practice
HighSchoolMathTeachers.com©2020 Page 91
Use the following statement to answer questions 1 – 15.
Use each diagram to answer two questions after it.
1. Identify the most common rigid motion(s) relating the two figures in present.
2. Identify the congruent sides
3. Identify the most common rigid motion(s) relating the two figures in present.
4. Identify the congruent sides
A B
C
D
E R
W
X
Z
Y
S
U
S Q
E
Y
X
L
Day 51 Practice
HighSchoolMathTeachers.com©2020 Page 92
5. Identify the most common rigid motion(s) relating the two figures in present.
6. Identify the congruent sides
7. Identify the most common rigid motion(s) relating the two figures in present.
8. Identify the congruent sides
9. Identify the most common rigid motion(s) relating the two figures in present.
W
E R
T
Y U
P A
S
D F
Day 51 Practice
HighSchoolMathTeachers.com©2020 Page 93
10. Identify the congruent sides
11. Identify the most common rigid motion(s) relating the two figures in present.
12. Identify the congruent sides
13. Identify a single rigid motion relating the two figures in present.
14. Identify the most common rigid motion(s) relating the two figures in present.
F
G
H
J
K
L
X Z
L K
H J
Day 51 Practice
HighSchoolMathTeachers.com©2020 Page 94
15. Identify the congruent sides based on the motion in 13 above.
Use the following image to answer questions 16 – 20
The figure below shows the motion of an equilateral triangle.
16. Identify one single rigid motion relating the two triangles above.
17. Identify the congruent sides for the rigid motion above
18. Identify another single rigid motion relating the two triangles above
19. Identify the congruent sides for the rigid motion above
20. Identify a single rigid motion that cannot map one triangle to the other in the figure above.
A
B
H
Y
C G
Day 51 Practice
HighSchoolMathTeachers.com©2020 Page 95
Answer Keys
Day 51
1. Rotation
2. AC and DR,CB and RE, and BA and ED
3. Glide reflection
4. WX and SU, XZ and UY, and ZW and YS
5. Rotation and translation
6. SQ and XY, QE and YL, and ES and LX
7. Translation
8. RE and UY, EW and YT, and WR and TU
9. Reflection
10. FS and PS, SD and SA, and DF and AP
11. Rotation
12. LK and JH, KG and HF, and GL and FJ
13. Glide reflection
14. Rotation and translation
15. HJ and XZ, JK and ZL, and KH and LX
16. Reflection or Translation
17. If reflection AB and HY, BC and YG, and CA and GH
If translation AB and GY, BC and YH, and CA and HG 18. Reflection or Translation
19. If reflection AB and HY, BC and YG, and CA and GH
If translation AB and GY, BC and YH, and CA and HG 20. Rotation
Day 51 Exit Slip
HighSchoolMathTeachers.com©2020 Page 96
Identify corresponding sides in the following triangles if they are related by a series of rigid motions.
M N
L
D
K
Z
Day 51 Exit Slip
HighSchoolMathTeachers.com©2020 Page 97
Answer Keys
Day 51
ML and DZ
LN and KD
MN and KZ
Day 52 Bellringer
HighSchoolMathTeachers.com©2020 Page 98
1. The diagram below shows Δ PQR mapped onto Δ XYZ after undergoing a rigid motion. Study it in
order to answer the questions that follow.
(a) Which type of rigid motion has mapped Δ PQR onto Δ XYZ above?
(b) Identify congruent sides from the pre-image and the image?
P
Q R
𝑙 X
Y Z
Day 52 Bellringer
HighSchoolMathTeachers.com©2020 Page 99
(c) Based on the type of rigid motion you have identified in (a) above, how does Δ PQR and Δ XYZ
compare?
2. Rectangle ABCD below has undergone a translation towards the right to form its image, rectangle
KLMN. Study the two rectangles and answer the following questions.
(a) Identify the corresponding sides on rectangles ABCD and KLMN above.
(b) Identify pairs of equal sides on rectangles ABCD and KLMN above.
A
B C
D K
L M
N
Day 52 Bellringer
HighSchoolMathTeachers.com©2020 Page 100
Answer Keys Day 52:
1. (a) A reflection
(b) PQ and XY; QR and YZ; PR and XZ
(c)Δ PQR ≅ Δ XYZ, they have the same shape and size
2. (a) AB and KL; BC and LM; CD and MN; AD and KN
(b) AB and KL; BC and LM; CD and MN; AD and KN
Day 52 Activity
HighSchoolMathTeachers.com©2020 Page 101
1. Using a ruler draw any triangle of a convenient size on the plain paper and label it ΔABC in the order
shown below.
2. Place the tracing paper on the plain paper and carefully trace ΔABC with the help of a straightedge.
Label the duplicate triangle ΔKLM in the order shown below.
3. Slide the tracing paper carefully over the plain paper until ΔABC and ΔKLM coincide. What does this
tell you about the relationship between their sizes and shapes?
4. Using a protractor measure ∠A then measure ∠K and write down their measures. What do you notice
about these two angles? Note the relative positions of the angles with reference to each other in the
two triangles.
5. Now measure ∠B then measure ∠L and write down their measures. What do you notice about these
two angles? Note the relative positions of the angles with reference to each other in the two triangles.
A
B C
K
L M
Day 52 Activity
HighSchoolMathTeachers.com©2020 Page 102
6. Similarly, measure ∠C then measure ∠M and write down their measures. What do you notice about
these two angles? Note the relative positions of the angles with reference to each other in the two
triangles.
7. If we were to measure the lengths of the corresponding sides using a ruler, just like we have
measured the angles, what is the most likely outcome?
Day 52 Activity
HighSchoolMathTeachers.com©2020 Page 103
In this activity students will work in groups of four to identify congruent angles in congruent triangles.
Students in the respective groups will require a protractor, a straightedge and A4 size tracing paper and
an A4 plain paper.
Answer Keys
Day 52:
1. No response
2. No response
3. They have the same size and shape? They are congruent
4. The angles are approximately equal. Students should note that these are corresponding angles.
5. The angles are approximately equal. Students should note that these are corresponding angles.
6. The angles are approximately equal. Students should note that these are corresponding angles.
7. The corresponding sides will have approximately the same length.
Day 52 Practice
HighSchoolMathTeachers.com©2020 Page 104
On the grid below Δ KLM has been mapped onto Δ PQR after a half turn about the origin (0,0). Study it
and answer questions 1-5.
1. Identify all pairs of corresponding sides.
2. Identify all pairs of corresponding angles.
3. Show the mapping of corresponding vertices.
K
L
y
x
M
−6 − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 6 7
P
Q R
Day 52 Practice
HighSchoolMathTeachers.com©2020 Page 105
4. Identify all pairs of congruent angles.
5. Basing on questions 1-4 above, what do you conclude about the two triangles?
The figure below shows two triangles. ΔPQR has been mapped to ΔABC after a translation. Study it and
use it to answer questions 6-10.
6. Identify all pairs of corresponding sides.
7. Identify all pairs of corresponding angles.
8. Identify all pairs of congruent angles.
9. Show the mapping of corresponding vertices.
10. What can you say about the sizes and the shapes of the two triangles with reference to each other?
A
B C
P
Q R
Day 52 Practice
HighSchoolMathTeachers.com©2020 Page 106
ΔPQR has been mapped to ΔKLM through a reflection along the mirror line 𝑙 as shown below. Study the
figure and use it to answer questions 11-15.
11. List all pairs of corresponding sides.
12. List all pairs of corresponding angles.
13. List all pairs of congruent angles.
14. Show the mapping of corresponding vertices.
15. According to what you have learnt on rigid motion do you expect the two triangles to be congruent?
Give a reason.
A
B C
P
Q R
𝑙
Day 52 Practice
HighSchoolMathTeachers.com©2020 Page 107
A student performed a glide reflection on ΔPQR and it was mapped onto ΔXYZ as shown below. Study
the student’s diagram and answer questions 16-20.
16. List all pairs of corresponding sides.
17. List all pairs of corresponding angles.
18. List all pairs of congruent angles.
X
Z Y
P
Q R
𝑙
Day 52 Practice
HighSchoolMathTeachers.com©2020 Page 108
19. Show the mapping of corresponding vertices.
20. Is the dotted triangle congruent to both ΔPQR and ΔXYZ? Give a reason.
Day 52 Practice
HighSchoolMathTeachers.com©2020 Page 109
Answer keys Day 52:
1. KL and PQ
LM and QR
KM and PR
2. ∠K and ∠P
∠L and ∠Q
∠M and ∠R
3. K → P
L → Q
M → R
4. ∠K and ∠P
∠L and ∠Q
∠M and ∠R
5. The two triangles are congruent.
6. AB and PR
BC and RQ
AC and PQ
7. ∠A and ∠P
∠B and ∠R
∠C and ∠Q
8. ∠A and ∠P
∠B and ∠R
∠C and ∠Q
9. A → P
B → R
C → Q
10. They have the same size and shape.
11. AB and PQ
BC and QR
AC and PR
12. ∠A and ∠P
∠B and ∠Q
∠C and ∠R
13. ∠A and ∠P
∠B and ∠Q
∠C and ∠R
14. A → P
B → Q
C → R
15. Yes. Rigid motion preserves distances.
16. PQ and XZ
QR and ZY
PR and XY
Day 52 Practice
HighSchoolMathTeachers.com©2020 Page 110
17. ∠P and ∠X
∠Qand ∠Z
∠R and ∠Y
18. ∠P and ∠X
∠Qand ∠Z
∠R and ∠Y
19. P → X
Q → Z
R → Y
20. Yes. Rigid motions preserve size and shape.
Day 52 Exit Slip
HighSchoolMathTeachers.com©2020 Page 111
On the grid below Δ PQR has been mapped onto Δ ABC after a half turn about the origin (0,0).
Considering Δ PQR and Δ ABC, identify all the pair of congruent angles.
P
Q
y
x
R
−6 − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 6 7
5
4
3
2
1
−1 A
C B
Day 52 Exit Slip
HighSchoolMathTeachers.com©2020 Page 112
Answer Keys
Day 52:
∠P ≅ ∠A
∠Q ≅ ∠C
∠R ≅ ∠B
Day 53 Bellringer
HighSchoolMathTeachers.com©2020 Page 113
1. State whether each of the following pairs of triangles is congruent or not.
a)
b)
Day 53 Bellringer
HighSchoolMathTeachers.com©2020 Page 114
c)
d)
2. A triangle is rotated clockwise about the origin and then reflected over the y-axis. Is the final image
congruent to the original triangle.
Day 53 Bellringer
HighSchoolMathTeachers.com©2020 Page 115
Answer Key Day 4
1. a) Yes
b) No
c) Yes
d) Yes
2. Yes
Day 53 Activity
HighSchoolMathTeachers.com©2020 Page 116
1. Place tile of the plane paper and draw its image accurately. Label it.
2. Lift it and place it at another position in any direction and draw its image accurately. Label it.
3. Before looking at the sides and angles, what makes you conclude that the two triangles drawn are
congruent?
4. Identify corresponding angle and sides
5. Measure all angles all sides
6. Compare corresponding angles. What do you notice about each pair of corresponding angles?
7. Measure the corresponding sides
8. What do you notice about each pair of corresponding sides?
9. Based on the results above, make a generalization of the features congruent triangles must satisfy.
Day 53 Activity
HighSchoolMathTeachers.com©2020 Page 117
In this activity, we would like to show that if two triangles are congruent, then they have corresponding
angles and sides. Students will work in groups of at least 5. Each group will a triangular small tile or a
triangular framework of rigid wires, a plane paper, ruler, protractor and a pencil.
Answer Keys
Day 53:
1 – 2. Different responses
3. They are congruent because drawn using the same tile
4 - 5. Different responses
6. They are equal
7. Different responses
9. They are equal
Day 53 Practice
HighSchoolMathTeachers.com©2020 Page 118
Questions 1 and 3 tests on the understanding of the theorem on congruence
State the conditions that two triangles must satisfy so that they may be congruent.
1. First Condition
2. Second condition
3. Given that the two conditions above are satisfied, what can we conclude about the scale factor if the
triangles?
4. Which transformations are used to show that two triangles are congruent?
Use the following statement to answer questions 5 – 14.
We want to prove that triangles ACB and QPR are congruent.
Fill the following table
STATEMENT REASON/ IDENTICATION
AC and QP, CB and PR, BA and RQ 5.
6. Corresponding angles
𝐴𝐶 = 𝑄𝑃, 𝐶𝐵 = 𝑃𝑅, 𝐵𝐴 = 𝑅𝑄 7.
∠𝐴 = ∠𝑄, ∠𝐶 = ∠𝑃, ∠𝐵 = ∠𝑅 8.
So far, the two triangles related by dilation 9. 𝐴𝐶
𝑄𝑃=
𝐶𝐵
𝑃𝑅=
𝐵𝐴
𝑅𝑄= 1
10.
Triangles have a linear scale factor of 1 𝟏𝟏.
The Area scale factor is also 1 12.
Triangles have equal area 13.
The triangles are congruent 14.
5
A
B
C
Q
R
P
10
10
5
8.7
8.7
60°
60° 30°
90°
Day 53 Practice
HighSchoolMathTeachers.com©2020 Page 119
Use the following statement to answer questions 15 – 18.
We would like to prove that the corresponding sides and angles of congruent triangles are equal if the
triangles are congruent.
Fill the following table
STATEMENT REASON/ IDENTICATION
The triangles are congruent 15. Given
One triangle can be mapped on the other after one or more rigid motions.
16.
Thus, corresponding angles are equal 17.
And corresponding angles are equal 18.
Use the following information to answer questions 19 – 20.
The two triangles above are congruent
19. Find the value of x
20. Find the length of KY.
Y
S K
Y
S K
2𝑥 + 1 𝑖𝑛
4𝑥 − 3 𝑖𝑛
Day 53 Practice
HighSchoolMathTeachers.com©2020 Page 120
Answer Keys
Day 53
1. Corresponding angles are equal or responding sides are equal
2. Corresponding angles are equal or responding sides are equal
3. 1
4. Glide reflection, reflection, rotation, translation
STATEMENT REASON/ IDENTICATION
AC and QP, CB and PR, BA and RQ 5. Corresponding angles
6. ∠𝑨 and ∠𝑸, ∠𝑪 𝐚𝐧𝐝 ∠𝑷, ∠𝑩 𝐚𝐧𝐝 ∠𝑹 Corresponding angles
𝐴𝐶 = 𝑄𝑃, 𝐶𝐵 = 𝑃𝑅, 𝐵𝐴 = 𝑅𝑄 7. Comparing their lengths
∠𝐴 = ∠𝑄, ∠𝐶 = ∠𝑃, ∠𝐵 = ∠𝑅 8. Comparing their angular measurements
So far, the two triangles related by dilation 9. Corresponding angles are equal
𝐴𝐶
𝑄𝑃=
𝐶𝐵
𝑃𝑅=
𝐵𝐴
𝑅𝑄= 1
10. Upon modification of 𝑨𝑪 = 𝑸𝑷, 𝑪𝑩 = 𝑷𝑹, 𝑩𝑨 = 𝑹𝑸
Triangles have a linear scale factor of 1 𝟏𝟏.
𝑨𝑪
𝑸𝑷=
𝑪𝑩
𝑷𝑹=
𝑩𝑨
𝑹𝑸= 𝟏
The Area scale factor is also 1 12. (𝒍𝒊𝒏𝒆𝒂𝒓 𝒔𝒄𝒂𝒍𝒆 𝒇𝒂𝒄𝒕𝒐𝒓)𝟐 =𝟏
Triangles have equal area 13. Area scale factor is 1
The triangles are congruent 14. Area scale factor is 1 and corresponding angles are equal
STATEMENT REASON/ IDENTICATION
The triangles are congruent 15. Given
One triangle can be mapped on the other after one or more rigid motions.
16. Properties of rigid motion
Thus, corresponding angles are equal 17. Properties of rigid motion
And corresponding angles are equal 18. Properties of rigid motion
19. 2 in 20. 5 in
Day 53 Exit Slip
HighSchoolMathTeachers.com©2020 Page 121
Based on the definition of congruence using rigid motion, Identify the condition that will make the two
triangles below to congruent.
R J
E
Q
F X
Day 53 Exit Slip
HighSchoolMathTeachers.com©2020 Page 122
Answer Keys
Day 53
The following angles and sides a must be equal
RE and XQ
EJ and QF
JR and FX
AND
Angles ∠𝐸 and ∠𝑄, ∠𝑅 and ∠𝑋, and ∠𝐹 and ∠𝐽
Day 54 Bellringer
HighSchoolMathTeachers.com©2020 Page 123
1. Use the figure below to answer the questions that follow. ∆𝐴𝐵′𝐶′ is an image of ∆𝐴𝐵𝐶.
a) Find the center of dilation.
b) Find the linear scale factor.
2. Points 𝐴(1,1), 𝐵(3,1), 𝐶(1,3), 𝐷(3,3) are vertices of a square. Taking the origin as the center of
dilation, find the vertices of the image when the scale factor is :
a) 2
b) 1
c) 3
𝐵′ 𝐵 A
𝐶′
C
1in
2in
Day 54 Bellringer
HighSchoolMathTeachers.com©2020 Page 124
Answer Key
Day 54
1. a) Point A
b) 1
2
2. a) 𝐴(2,2), 𝐵(6,2), 𝐶(2,6), 𝐷(6,6)
b) 𝐴(1,1), 𝐵(3,1), 𝐶(1,3), 𝐷(3,3)
c) 𝐴(3,3), 𝐵(9,3), 𝐶(3,9), 𝐷(9,9)
Day 54 Activity
HighSchoolMathTeachers.com©2020 Page 125
1. Plot a graph with a scale of 1 square representing 1 unit as shown.
2. Draw a triangle with vertices at points A(1,2), B(6,1) and C(4,4) as shown
Day 54 Activity
HighSchoolMathTeachers.com©2020 Page 126
3. Draw straight lines A to pass through the origin.
4. Position the compass at the origin and extend it to point A then using the same width make an arc on
opposite side to cross the line as shown.
5. Draw lines from points B and C through the origin and on each line, repeat step 3 as shown below.
Day 54 Activity
HighSchoolMathTeachers.com©2020 Page 127
6. Join the intersections of the arcs with straight lines as shown below.
7. Measure the distance of each point from the origin with its image distance from the origin.
8. Are they equal?
-6 -4 -2 0 2 4 6 x
y
4
2
-2
-4
A
B
C
Day 54 Activity
HighSchoolMathTeachers.com©2020 Page 128
In this activity students will draw a triangle and its image under a dilation with a scale factor of -1.
Student will work in groups of at least three and each group is required to have a graph paper, a pencil,
a ruler and a compass.
Answer Keys
Day 54:
1-6. No response
7. Different responses
8. Yes
Day 54 Practice
HighSchoolMathTeachers.com©2020 Page 129
Use the diagram below to answer questions 1-3.
The rectangle below is dilated with a scale factor of -1 about point R.
(the figure is not drawn to scale)
1. Draw the image
2. Find the distance 𝑅𝑇′
3. Find the distance 𝑈𝑈′
∆𝑀𝑁𝑂 is dilated with a scale factor of -1 about point P. The distances MP, NP and OP are 3in, 2in and
5in respectively. Use this information to answer questions 4-6.
4. What is the distance of 𝑂𝑃′?
5. What is the distance of 𝑁𝑃′?
6. What is the distance of 𝑀𝑃?
R
U T
S
6𝑖𝑛
8𝑖𝑛
Day 54 Practice
HighSchoolMathTeachers.com©2020 Page 130
Use the graph below to answer questions 7-19. ∆𝐴𝐵𝐶 is dilated with a scale factor of -1 with the center
at the origin.
7. What will be the coordinates of the image of point A?
8. What will be the coordinates of the image of point B?
9. What will be the coordinates of the image of point C?
10. On the graph, indicate the image of ∆𝐴𝐵𝐶.
-6 -4 -2 0 2 4 6 x
y
4
2
-2
-4
A
B
C
O
Day 54 Practice
HighSchoolMathTeachers.com©2020 Page 131
With respect to the graph have drawn in question 10 above, state whether the statements in questions
11-14 are true or false.
11. The distances OB and 𝑂𝐵′ are equal.
12. 𝑂𝐵 =1
2𝐵𝐵′
13. 1
2𝑂𝐴 = 𝐴𝐴′
14. 𝑂𝐶 = 𝑂𝐶′
15. 1
2𝑂𝐶 = 𝐶𝐶′
16. 𝑂𝐴 ≅ 𝑂𝐴′
17. 𝑂𝐵 ≅ 𝑂𝐵′
18. 𝑂𝐶 ≅ 𝑂𝐶′
19. 𝑂𝐵 ≅ 𝐵𝐵′
20. The triangle below is translated with a scale factor of -1 and center O. Indicate the image.
O
Day 54 Practice
HighSchoolMathTeachers.com©2020 Page 132
Answer Key
Day 54:
1.
2. 10𝑖𝑛
3. 12𝑖𝑛
4. 5𝑖𝑛
5. 2𝑖𝑛
6. 3𝑖𝑛
7. (−1, −1)
8. (−4, −2)
9. (−1, −4)
R
U T
S
6𝑖𝑛
8𝑖𝑛
𝑇′ 𝑈′
𝑅′ 𝑆′
Day 54 Practice
HighSchoolMathTeachers.com©2020 Page 133
10.
11. True
12. True
13. False
14. False
15. False
16. True
17. True
18. True
19. False
20.
-6 -4 -2 0 2 4 6 x
y
4
2
-2
-4
A
B
C
𝐴′
𝐶′
𝐵′
O
Day 54 Exit Slip
HighSchoolMathTeachers.com©2020 Page 134
The triangle below is dilated about point P with a scale factor of -1. Indicate the image.
P
Day 54 Exit Slip
HighSchoolMathTeachers.com©2020 Page 135
Answer Keys
Day 54:
P
136
High School Math Teachers
Geometry
Weekly Assessment Package
Week 11
©2020HighSchoolMathTeachers
137
Week 11
Weekly Assessments
138
Week #11 1. Use the triangles below to answer the
questions that follow
a) Which rigid motion will map the two
triangle onto each other?
b) What is the size of ∠𝑀?
c) What is the size of ∠𝑂?
d) Is ∆𝐴𝐵𝐶 ≅ ∆𝑀𝑁𝑂?
2. Construct squares inscribed in each circle below.
a) A circle with a radius of 0.8 𝑖𝑛. b) A circle with a radius of 1 𝑖𝑛.
A B M N
O C
60°
139
3. ∆𝐴𝐵𝐶 is dilated about point C with a scale factor of -1 as shown. a) What is the length of 𝐴′𝐶? b) What is the length of 𝐵′𝐶? c) What is the length of 𝐴′𝐵′? d) Is ∆𝐴𝐵𝐶 ≅ ∆𝐴′𝐵′𝐶?
4. Use the diagram below to answer the questions that follow. a) Which rigid motion will map the triangles above onto each other? b) Which side is congruent to AC? C) Which side is congruent to AB? d) Which angle is congruent to ∠𝐶?
A
B
C
𝐴′
𝐵′ 2.5 𝑖𝑛
3 𝑖𝑛
1.8 𝑖𝑛 A B
C
M N
O
140
5. Use the triangles below to answer the questions that follow. a) State whether the triangles above are congruent. b) Give a reason for the answer you gave in (a) above.
6. Use the diagram below to answer the questions that follow. a) State a single rigid motion that will map the two rectangles. b) Describe a series of reflections that will map the two rectangles.
2 𝑖𝑛
4 𝑖𝑛
4 𝑖𝑛
3 𝑖𝑛
5 𝑖𝑛
𝐴 𝐵
𝐷 𝐶
𝐵′ 𝐴′
𝐶′ 𝐷′
141
Week 11 - Keys
Weekly Assessments
142
Week #11 KEY
3. Use the triangles below to answer the
questions that follow
e) Which rigid motion will map the two
triangle onto each other?
Reflection f) What is the size of ∠𝑀?
60°
g) What is the size of ∠𝑂?
30°
h) Is ∆𝐴𝐵𝐶 ≅ ∆𝑀𝑁𝑂?
Yes
4. Construct squares inscribed in each circle below.
a) A circle with a radius of 0.8 𝑖𝑛. b) A circle with a radius of 1 𝑖𝑛.
A B M N
O C
60°
143
3. ∆𝐴𝐵𝐶 is dilated about point C with a scale factor of -1 as shown. a) What is the length of 𝐴′𝐶? 2.5 𝑖𝑛 b) What is the length of 𝐵′𝐶? 1.8 𝑖𝑛 c) What is the length of 𝐴′𝐵′? 3 𝑖𝑛 d) Is ∆𝐴𝐵𝐶 ≅ ∆𝐴′𝐵′𝐶? Yes
4. Use the diagram below to answer the questions that follow. a) Which rigid motion will map the triangles above onto each other? Glide reflection b) Which side is congruent to AC? MO C) Which side is congruent to AB? MN d) Which angle is congruent to ∠𝐶?
∠𝑂
A
B
C
𝐴′
𝐵′ 2.5 𝑖𝑛
3 𝑖𝑛
1.8 𝑖𝑛 A B
C
M N
O
144
5. Use the triangles below to answer the questions that follow. a) State whether the triangles above are congruent. They are not congruent b) Give a reason for the answer you gave in (a) above. All coresponding sides are not equal.
6. Use the diagram below to answer the questions that follow. a) State a single rigid motion that will map the two rectangles. A reflection b) Describe a series of reflections that will map the two rectangles. A reflection over a horizontal mirror line below ABCD followed a reflection over a vertical mirror line on the right then a reflection over a horizontal mirror line.
2 𝑖𝑛
4 𝑖𝑛
4 𝑖𝑛
3 𝑖𝑛
5 𝑖𝑛
𝐴 𝐵
𝐷 𝐶
𝐵′ 𝐴′
𝐶′ 𝐷′
Day 56 Bellringer
HighSchoolMathTeachers.com©2020 Page 145
ΔABC is mapped onto ΔPQR after a translation to the right as shown below. Identify angles and sides
corresponding to the ones indicated.
(a) AB̅̅ ̅̅
(b) QR̅̅ ̅̅
(c) AC̅̅̅̅
(d) ∠P
(e) ∠B
(f) ∠C
A
B C
P
Q R
Day 56 Bellringer
HighSchoolMathTeachers.com©2020 Page 146
Answer Keys
Day 56:
(a) PQ̅̅̅̅
(b) BC̅̅̅̅
(c) PR̅̅̅̅
(d) ∠A
(e) ∠Q
(f) ∠R
Day 56 Activity
HighSchoolMathTeachers.com©2020 Page 147
1. Using a ruler draw any triangle of a convenient size on the plain paper and label it ΔPQR in the order
shown below.
2. Place the tracing paper on the plain paper and carefully trace ΔPQR with the help of a straightedge.
Label the duplicate triangle ΔXYZ in the order shown below.
3. Assuming that ΔPQR is mapped onto ΔXYZ by a translation, identify all pairs of corresponding sides
from the triangles.
4. Using a ruler, measure the length of each side in all the corresponding pairs of sides you have
identified in question 3 above in inches and write down the measurements. What do you notice about
the relationship between the lengths of corresponding sides?
5. What can you say about the relationship between the length of corresponding sides in ΔPQR and
ΔXYZ and the congruency of these triangles?
P
Q R
X Y
Z
Day 56 Activity
HighSchoolMathTeachers.com©2020 Page 148
In this activity students will work in groups of at least four to discover the congruence postulate SSS
using congruent triangles. Each groups will require a ruler, an A4 size tracing paper and an A4 plain
paper.
Answer Keys
Day 56:
1. No response
2. No response
3. PQ and ZX
QR and XY
PR and ZY
4. All the corresponding sides have the same length; all the corresponding sides are congruent.
5. All the corresponding sides in the two triangles are congruent hence the two triangles are congruent.
Day 56 Practice
HighSchoolMathTeachers.com©2020 Page 149
The pairs of triangles in questions 1-5 are congruent. Find the length of the left-out third side. All the
measurements are in inches. Note that the triangles are not drawn to scale.
1.
2.
7 9 9
8 8
13
13
12
10
12
Day 56 Practice
HighSchoolMathTeachers.com©2020 Page 150
3.
4.
4
6
5
6 5
4 4
14
13
13
Day 56 Practice
HighSchoolMathTeachers.com©2020 Page 151
5.
6. The figure below shows parallelogram PQRS, identify two pairs of congruent triangles using the SSS
postulate.
7. The figure below shows square JKLM. Show that ΔJLK ≅ ΔJLK using the SSS postulate.
8
8
10
5
10
P
Q R
S
T
J
K L
M
Day 56 Practice
HighSchoolMathTeachers.com©2020 Page 152
The figure below shows two congruent triangles, ΔABC and ΔADE. Use it to answer questions 8 and 9.
8. List all pairs of corresponding sides of the two triangles.
9. Show that the two triangles are congruent.
A
B C
D E 6 in.
6 in. 10 in.
10 in.
Day 56 Practice
HighSchoolMathTeachers.com©2020 Page 153
Use the figure below to answer questions 10-16. PQ̅̅̅̅ ≅ PR̅̅̅̅ and PT̅̅̅̅ bisects QR̅̅ ̅̅ .
10. Identify two congruent triangles in the figure above.
11. List the pairs of corresponding sides in the two triangles you have identified in question 10 above.
Complete the table below using the figure above.
Statement Reason
PQ̅̅̅̅ ≅ PR̅̅̅̅ Given
12. Given
Point T is the midpoint of QR̅̅ ̅̅ 13.
QT̅̅ ̅̅ ≅ RT̅̅̅̅ 14.
15. Reflexive property
16. The S.S.S postulate
P
Q R T
Day 56 Practice
HighSchoolMathTeachers.com©2020 Page 154
Study the figure below and use it to answer questions 17-20. Point C is the common point of the two
triangles.
Complete the table below by identify a side corresponding to the one given
AB̅̅ ̅̅ 17.
18. DE̅̅ ̅̅
19. If BC̅̅̅̅ ≅ CD̅̅̅̅ , state whether these triangles will be congruent or not.
20. Give a reason for you answer to question 19 above.
A
B
C
D
E
Day 56 Practice
HighSchoolMathTeachers.com©2020 Page 155
Answer keys
Day 56:
1. 7 in.
2. 10 in.
3. 4 in.
4. 14 in.
5. 5 in.
6. ΔPTS and ΔQTR
ΔPTQ and ΔRTS
ΔPQS and ΔQRS
ΔPRS and ΔPQR
7. JM̅̅̅̅ ≅ LK̅̅̅̅ (opposite sides of a square are congruent)
ML̅̅ ̅̅ ≅ KJ̅ (opposite sides of a square are congruent)
JL̅ ≅ LJ̅ (Reflexive property)
Therefore S.S.S postulate satisfied.
8. BC̅̅̅̅ and AC̅̅ ̅̅
AC̅̅̅̅ and DE̅̅ ̅̅̅
AB̅̅ ̅̅ and DA̅̅ ̅̅̅
9 . BC̅̅̅̅ ≅ AC̅̅ ̅̅ (Given)
AC̅̅̅̅ ≅ DE̅̅ ̅̅̅ = 6 𝑖𝑛
AB̅̅ ̅̅ ≅ DA̅̅ ̅̅̅ = 10 𝑖𝑛. The S.S.S postulate is achieved.
10. ΔPQT and ΔPRT
Day 56 Practice
HighSchoolMathTeachers.com©2020 Page 156
11. PT̅̅̅̅ and PT̅̅̅̅
PQ̅̅̅̅ and PR̅̅ ̅̅
QT̅̅ ̅̅ and RT̅̅̅̅̅
12.
Statement Reason
PQ̅̅̅̅ ≅ PR̅̅̅̅ Given
12. 𝐏𝐓̅̅ ̅̅ bisects QR Given
Point T is the midpoint of QR̅̅ ̅̅ 13. 𝐏𝐓̅̅ ̅̅ is the perpendicular bisector of 𝐐𝐑̅̅ ̅̅ ̅
QT̅̅ ̅̅ ≅ RT̅̅̅̅ 14.T is the midpoint of 𝐐𝐑̅̅ ̅̅
15. 𝐏𝐓̅̅ ̅̅ ≅ 𝐏𝐓̅̅ ̅̅ Reflexive property
16. 𝚫𝐏𝐐𝐓 and 𝚫𝐏𝐑𝐓 The S.S.S postulate
17.
AB̅̅ ̅̅ 17. 𝐂𝐄̅̅̅̅
18. 𝐂𝐀̅̅ ̅̅ DE̅̅ ̅̅
19. They will be congruent.
20. All the three corresponding sides will be congruent/ according to the S.S.S postulate.
Day 56 Exit Slip
HighSchoolMathTeachers.com©2020 Page 157
Consider triangles ΔXYZ and ΔKLM. The measurements are in inches.
Are the two triangles congruent? If so, show why?
5
3
5 3
4
4
X
Y Z
K
L
M
Day 56 Exit Slip
HighSchoolMathTeachers.com©2020 Page 158
Answer Keys Day 56:
Yes.
XY̅̅̅̅ = MK̅̅̅̅̅ = 3 𝑢𝑛𝑖𝑡𝑠
YZ̅̅̅̅ = KL̅̅̅̅ = 4 𝑢𝑛𝑖𝑡𝑠
XZ̅̅̅̅ = ML̅̅ ̅̅ = 5 𝑢𝑛𝑖𝑡𝑠.
SSS postulate is achieved thus ΔXYZ ≅ ΔKLM
Day 57 Bellringer
HighSchoolMathTeachers.com©2020 Page 159
1. Find the third angle of a triangle whose angles are given below.
(i). 77° 𝑎𝑛𝑑 46°
(ii). 63° 𝑎𝑛𝑑 81°
(iii). 92° 𝑎𝑛𝑑 64°
2. Given that the corresponding sides of a triangle are 12 𝑖𝑛 and 15 𝑖𝑛 respectively.
(i). Find the linear scale factor relating the two given the smaller triangle is the image of the larger one.
(ii). Find the measurement of the other side of the smaller triangle is the corresponding side of the
bigger ttriangle is 25 in.
Day 57 Bellringer
HighSchoolMathTeachers.com©2020 Page 160
Answer Key
Day 57
1. (i). 57°
(ii). 36°
(iii). 24°
2. (i) 4
5
(ii). 20𝑖𝑛
Day 57 Activity
HighSchoolMathTeachers.com©2020 Page 161
1. Draw a 4 in line and label it TY.
2. Using a protractor, construct an angle of 30° and 60° at T and Y respectively.
3. Let the lines from T and Y meet respectively at U.
4. Draw another 4 in line and label it PR.
5. Using a protractor, construct an angle of 30° and 60° at P and R respectively.
6. Let the lines from P and R meet respectively at W.
7. Measure the angles at U and W respectively, record your answer.
8. How are the angles in 7 above related?
9. Measure the length of lines TU and YU, as well as PW and RW, record your answer.
10. Find the area of triangles TYU and PRW.
11. Compare the areas in 10 above.
12. Make the conclusions about the results based on the information provided.
Day 57 Activity
HighSchoolMathTeachers.com©2020 Page 162
In this activity, we would like to prove by construction that the postulate ASA is true, that is, once a
triangles satisfy the postulate, then the triangles inclined are congruent. Students will work in groups of
at least 3. Each group will need A4 plain paper, protractor, a ruler and a pencil.
Answer Keys
Day 57:
1 – 6.No response
7. ∠𝑈 = 90°, ∠𝑊 = 90
8. The angles are equal
9. 𝑇𝑈 = 3.5 in and 𝑌𝑈 = 2 𝑖𝑛
𝑃𝑊 = 3.5 in and 𝑅𝑊 = 2 𝑖𝑛
10. 𝑇𝑌𝑈 = 3.5 𝑠𝑞 𝑖𝑛 and 𝑃𝑅𝑊 = 3.5𝑠𝑞. 𝑖𝑛.
11.They are equal
12. Given two triangles whose two corresponding lines and corresponding angles at the end points are
equal, the triangles are congruent.
Day 57 Practice
HighSchoolMathTeachers.com©2020 Page 163
1. Identify a property that is shared between dilated images those that are congruent.
2. Two images are related by a scale factor of 1, what would be the transformation between them?
Name all of them.
Use the following information to answer questions 3 - 5.
Two triangles are such that corresponding sides are congruent
3. Are they equilateral triangles? Why?
4. Comment of their angles
5. Is ASA satisfied?
6. Explain the answer above.
Use the following diagrams to answer questions 7 - 10 .
7. Identify all pairs of corresponding angles
Q P
F
B
T
G
6 6
Day 57 Practice
HighSchoolMathTeachers.com©2020 Page 164
8. Identify all pairs of corresponding sides
9. Based on ASA postulate, are the triangle congruent?
10. Explain your answer in 9 above.
Use the following diagrams to answer questions 11 – 14.
11. Identify all pairs of corresponding angles
12. Identify all pairs of corresponding sides
13. Based on ASA postulate, are the triangle congruent?
14. Explain your answer in 13 above.
X
U
D
9
12
B 12
Day 57 Practice
HighSchoolMathTeachers.com©2020 Page 165
Use the following diagram to answer questions 15 – 18.
In the figure below, SVR is an Isosceles triangle and J is the midpoint of line SR.
15. Write a relation between lines SJ and JR.
16. Write a relation between the angles SVR and JVR.
17. Identify all pairs of corresponding angles in triangle SVJ and JVR.
18. Identify all pairs of corresponding sides in triangle SVJ and JVR.
19. Based on ASA postulate, are the triangle, SVJ and JVR, congruent?
20. Explain your answer in 15 above.
S
V
R
J
Day 57 Practice
HighSchoolMathTeachers.com©2020 Page 166
Answer Keys
Day 57
1. Corresponding angles are equal
2. Reflection, rotation, glide reflection, translation and dilation of scale factor 1
3. No, No enough information is given to confirm if they are equilateral triangles
4. Corresponding angles are equal
5. Yes
6. Since all corresponding sides are equal, we pick just one side. Since corresponding angles are
equal, the corresponding angles the end points of the chosen side will be congruent hence ASA
is satisfied.
7. QF and TB, FP and BG, and PQ and GT
8. ∠𝑄 and ∠𝑇, ∠𝐹 and ∠𝐵, ∠𝐺 and ∠𝑃
9. No
10. Corresponding angles equal, but no enough information on corresponding sides
11. ∠𝑋 and ∠𝑉, ∠𝑈 and ∠𝑁, ∠𝐷 and ∠𝐵
12. XU and VN, DU and NB, and DX and BV
13. YES
14. Corresponding sides DX and BV are equal and corresponding angles at their endpoints are
congruent
15. 𝑆𝐽 = 𝐽𝑅
16. ∠𝑆𝑉𝑅 = 2∠𝐽𝑉𝑅
17. ∠𝑅𝐽𝑉 and ∠𝑉𝐽𝑆, ∠𝑆 and ∠𝑅, ∠𝑅𝑉𝐽 and ∠𝐽𝑉𝑆
18. VJ and VJ (Common), JR and SJ, and RV and SV
19. Yes
20. Sides RV and SV are equal (Given). Since triangle SVR is Isosceles, and J is the midpoint of RS, JV
is the bisector of angle SVR, hence ∠𝑅𝑉𝐽 = ∠𝐽𝑉𝑆 and ∠𝑆 = ∠𝑅 being base angles of the
Isosceles triangle.
Hence ASA is achieved.
Day 57 Exit Slip
HighSchoolMathTeachers.com©2020 Page 167
Identify a reason based on ASA postulate that will make the triangles not congruent.
55°
25°
4 in
25°
55°
4 in
Day 57 Exit Slip
HighSchoolMathTeachers.com©2020 Page 168
Answer Keys
Day 57
Corresponding angles at the end points of the line equal to 4in are not congruent
Day 58 Bellringer
HighSchoolMathTeachers.com©2020 Page 169
Find out if the two triangles given are congruent, hence identify the postulate used.
1.
2.
3.
t t
13
13
H
L
T
V
R
7
15°
7
15°
18°
4
18° 8
76°
86° 86°
76°
Day 58 Bellringer
HighSchoolMathTeachers.com©2020 Page 170
Identify an included angle with respect to the sides whose measurements are given
4.
5.
A
S N
7 units
6.2 units
E
B
M
4.7
9.3
Day 58 Bellringer
HighSchoolMathTeachers.com©2020 Page 171
Answer Key
Day 58
1. (i). They are congruent. Postulate SSS
(ii). They are congruent. Postulate ASA
(iii). They are not congruent
No two pairs of corresponding sides are given to help us establish the postulate
2. (i). Angle ANS
(ii). Angle BME
Day 58 Activity
HighSchoolMathTeachers.com©2020 Page 172
1. Draw a 3.5 in line and label it AB.
2. Using a protractor, construct an angle of 90° at B.
3. Locate C so that BC is 6 in. Connect C to A
4. Draw another 3.5 in line and label it XY.
5. Using a protractor, construct an angle of 90° at Y..
6. Locate Z so that YZ is 6 in. Connect Z to X
7. Measure the angles at A and C respectively, record your answer.
8. Measure the angles at X and Z respectively, record your answer.
9. What do you conclude about the angles of the two triangles?
10. Find the area of the two triangles.
11.Compare the areas in 10 above.
12. Make the conclusions about the results based on the information provided.
Day 58 Activity
HighSchoolMathTeachers.com©2020 Page 173
In this activity, we would like to prove by construction that the postulate SAS is true, that is, once a
triangles satisfy the postulate, then the triangles inclined are congruent. Students will work in groups of
at least 3. Each group will need A4 plain paper, protractor, a ruler and a pencil.
Answer Keys
Day 58:
1 – 6. No response
7. ∠𝐴 ≈ 60°, ∠𝐶 ≈ 30°
8.Corresponding angles are equal
9. Area of 𝐴𝐵𝐶 = 10.5 𝑠𝑞 𝑖𝑛 and Area of 𝑋𝑌𝑍 = 10.5𝑠𝑞. 𝑖𝑛.
11.They are equal
12. Given two triangles whose at least one corresponding angles are equal and the corresponding sides
bounding the angles are equal, then the triangles are congruent.
Day 58 Practice
HighSchoolMathTeachers.com©2020 Page 174
Use SAS postulate to answer the following questions.
Use the diagrams above to answer questions 1 and 2
1. Are the two triangles above congruent?
2. Explain your answer.
Use the following information to answer questions 3 - 4.
3. Are the two triangles above congruent?
4. Explain your answer.
28°
7 11
28°
11
7
24°
12
6
24°
12
6
Day 58 Practice
HighSchoolMathTeachers.com©2020 Page 175
Use the following diagrams to answer questions 5 - 7 .
5. Find the value of 𝑡.
6. Are the two triangles, above, congruent?
7. Explain your answer
Use the following diagrams to answer questions 8 - 14.
8. Find the size of angle T and V.
9. If 𝑈𝑇 =2
√3, find the value of ST.
60°
30° S
T
U
V
W
X
Day 58 Practice
HighSchoolMathTeachers.com©2020 Page 176
10. If 𝑈𝑇 =2
√3, find the value of VW.
11. Find the value of WX.
12. What is the relationship between US and VX?
13. Find the value if VX.
14. Are the two triangle congruent?
15. Using SAS postulate where angle TSU is one of the included angle, prove your results in 13 above.
Use the following diagrams to answer questions 16 – 20.
We have that QR =2 in.
16. Find the length of RY.
45°
45° Y
Q
R
P
L
J
Day 58 Practice
HighSchoolMathTeachers.com©2020 Page 177
17. Find the length of JP.
18. Find the length of PL
19. Find the area of both triangles
20. Make a conclusion based on the information given in before 16 above.
Day 58 Practice
HighSchoolMathTeachers.com©2020 Page 178
Answer Keys
Day 58
1. YES
2. Two Corresponding sides and the corresponding included angle are congruent.
3. YES
4. Two Corresponding sides and the corresponding included angle are congruent.
5. 𝑡 = 112°
6. No
7. The corresponding included angles are not congruent
8. ∠𝑇 = 60°, ∠𝑉 = 30°
9. 4
√2
10. 2
11. 2
√3
12. No direct relationship before congruency is set up
13. 4
√2
14. Yes
15. 𝑈𝑇 = 𝑋𝑊 =2
√3
𝑈𝑆 = 𝑉𝑊(𝐺𝑖𝑣𝑒𝑛) 𝐼𝑛𝑐𝑙𝑢𝑑𝑒𝑑 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑎𝑛𝑔𝑙𝑒𝑠 𝑎𝑟𝑒 𝑒𝑞𝑢𝑎𝑙 Thus, SAS is satisfied
16. 2 in
17. 2 in
18. 2 in
19. Area of ∆𝑌𝑄𝑅 = 2 sq. in, Area of ∆𝐽𝑃𝐿 = 2 sq. in,
20. Right triangles whose pair of corresponding sides and angles are equal are congruent
Day 58 Exit Slip
HighSchoolMathTeachers.com©2020 Page 179
Use SAS postulate to show that the triangles are congruent. Explain.
8 in
8 in
87°
48°
5in
A
B
C
87°
45°
5in
D
T
Y
Day 58 Exit Slip
HighSchoolMathTeachers.com©2020 Page 180
Answer Keys
Day 58
∠𝐴 = ∠𝐷 = 180° − 87° − 45° = 48°
Corresponding sides are equal, 𝐵𝐴 = 𝑇𝐷 = 5 𝑖𝑛, 𝐴𝐶 = 𝐷𝑌 = 8 𝑖𝑛
Thus, the postulate, SAS is satisfied implying that the triangles are congruent.
Day 59 Bellringer
HighSchoolMathTeachers.com©2020 Page 181
1. (a) Identify the included angle between PR̅̅̅̅ and QR̅̅ ̅̅ in ΔPQR below.
(b) Identify the included side between ∠𝑋 and ∠𝑌 in ΔXYZ below.
2. State the congruence postulate that makes the following triangles congruent.
(a)
P
Q
R
Y Z
X
Day 59 Bellringer
HighSchoolMathTeachers.com©2020 Page 182
(b)
(c)
Day 59 Bellringer
HighSchoolMathTeachers.com©2020 Page 183
Answer Keys
Day 59:
1. (a) ∠R
(b) XY̅̅̅̅
2. (a) S.A.S
(b) A.S.A
(c) S.S.S
Day 59 Activity
HighSchoolMathTeachers.com©2020 Page 184
1. Using a ruler draw any triangle of convenient size on the plain paper provided and label it ΔABC.
Follow the order shown below.
2. Using a tracing paper, duplicate ΔABC and label it ΔKLM in the order shown below.
3. Using a ruler, measure the length of all the corresponding sides on ΔABC and ΔKLM and write down
their lengths. Compare the lengths of the corresponding sides and write down your conclusion.
4. Which triangle congruence postulate has been investigated in question 3 above?
5. Identify the included angle between sides AB and BC on ΔABC.
6. Similarly, identify the included angle between sides KL and LM on ΔKLM.
7. Measure each of the two included angles you have identified in questions 5 and 6 above using a
protractor. What do you notice?
A
B C
K
L M
Day 59 Activity
HighSchoolMathTeachers.com©2020 Page 185
8. Basing on questions 5-7 above, which triangle congruence postulate is being investigated?
9. Identify the included side between ∠A and ∠B on ΔABC
10. Similarly, identify the included side between ∠K and ∠L on ΔKLM.
11. Use a protractor to measure ∠A and ∠K and compare their measures. What do you notice?
12. Measure the length of each of the two included sides you have identified in questions 9 and 10
above using a ruler and compare their lengths. What do you notice?
13. Basing on questions 9-12, which triangle congruence postulate is being investigated?
14. Considering the steps above, state whether the two triangles are congruent or not? Give a possible
reason.
Day 59 Activity
HighSchoolMathTeachers.com©2020 Page 186
In this activity students will work in groups of two to four to verify the triangle congruence postulates,
S.S.S, S.A.S and A.S.A. Students in the groups will require a ruler, a protractor, a tracing paper of A4 size,
a plain paper of A4 size.
Answer Keys Day 59:
1. No response
2. No response
3. The corresponding sides are congruent
4. S.S.S postulate
5. ∠B
6. ∠L
7. The angles are congruent
8. S.A.S postulate
9. AB̅̅ ̅̅
10. KL̅̅̅̅
11. ∠A ≅ ∠K
12. They are congruent
13. A.S.A postulate.
14. They are congruent. The triangle congruence postulates are achieved.
Day 59 Practice
HighSchoolMathTeachers.com©2020 Page 187
For questions 1-3, use the triangle congruence postulate indicated to mark the triangles given that in
each case. ΔPQR ≅ ΔKLM.
1. S.S.S
2. S.A.S
3. A.S.A
P
Q M L
K
R
P
Q M L
K
R
P
Q M L
K
R
Day 59 Practice
HighSchoolMathTeachers.com©2020 Page 188
In questions 4 -10, identify a congruent triangle to the one indicated based. In each case name the
triangle using proper correspondence.
4. ΔPQR
5. ΔABD
6. ΔKLM
P
Q R S
A
B C
D
K
L M
N
Day 59 Practice
HighSchoolMathTeachers.com©2020 Page 189
7. ΔABF
8. ΔPSR
9. ΔJML
A
B
C D
F
P
Q R
S
K
J
L
M
Day 59 Practice
HighSchoolMathTeachers.com©2020 Page 190
10. ΔWXY
In questions 11-14, state whether the triangles are congruent or not based on the information given for
each. If congruent, identify the congruence postulate used.
11.
12. ΔKLM
W
X
Z
Y
P
Q M L
K
R
S
T U
V
Day 59 Practice
HighSchoolMathTeachers.com©2020 Page 191
13.
14.
Given that the two triangles are congruent, find the values of the unknown letters in questions 15-20.
P
Q
M L
K R
𝑡 + 4.5
2𝑎
100° 3𝑏 − 3 2𝑐 + 4
112°
87°
3𝑑 2.4 in.
2𝑡 + 3
2𝑓 5.6 𝑖𝑛
Day 59 Practice
HighSchoolMathTeachers.com©2020 Page 192
15. a
16. b
17. c
18. d
19. 𝑡
20. f
Day 59 Practice
HighSchoolMathTeachers.com©2020 Page 193
Answer keys Day 59:
1. (In other marking that implies SSS can do)
2. (In other marking that implies SAS can do)
3. (In other marking that implies ASA can do)
P
Q M L
K
R
P
Q M L
K
R
P
Q M L
K
R
Day 59 Practice
HighSchoolMathTeachers.com©2020 Page 194
4. ΔPSR
5. ΔCDB
6. ΔNML
7. ΔDBC
8. ΔRPQ
9. ΔJKL
10. ΔWZY
11. Congruent. S.A.A
12. Not congruent
13. Congruent S.S.S.
14. Congruent A.S.A
15. 𝑡 = 56°
16. 𝑏 = 30°
17.𝑐 = 48°
18. 0.8 in.
19. 1.5 in.
20. 2.8 in.
Day 59 Exit Slip
HighSchoolMathTeachers.com©2020 Page 195
Use the figure below to answer the following questions.
Given that AB̅̅ ̅̅ ≅ ED̅̅ ̅̅ ; AC̅̅̅̅ ≅ EC̅̅̅̅ and ∠A ≅ ∠E.
(a) Name the triangle which is congruent to ΔEDC.
(b) Using the information given above, which triangle congruence postulate has been used to show that
the two triangles are congruent?
A
B C D
E
Day 59 Exit Slip
HighSchoolMathTeachers.com©2020 Page 196
Answer Keys
Day 59:
(a) ΔABC
(b) S.A.S postulate
197
High School Math Teachers
Geometry
Weekly Assessment Package
Week 12
©2020HighSchoolMathTeachers
198
Week 12
Weekly Assessments
199
Week #12 1. Use the triangles below to answer the
questions that follow.
a) Which side corresponds to ST?
b) Which side corresponds to TU?
2. Identify the fixed points in the following
transformations.
a) A square reflected over its diagonal. b) A rectangle translated to the left by two units.
3. Use the diagram below to answer the questions
that follow. C is the midpoint of BD.
a) Which corresponds to BC? b) Show that ∆𝐴𝐵𝐶 ≅ ∆𝐴𝐷𝐶.
4. State whether the pairs of triangles are
congruent or not.
a) a)
60°
85° 35° S
T
U
60°
M
85°
N
O
A
B
C
D
2.2 𝑖𝑛 2.1 𝑖𝑛
200
5. Identify the postulate making each pair of the
triangles congruent.
a) b)
6. The triangles below are congruent.
a) Which angle corresponds to ∠𝐷? b) Which angle corresponds to ∠𝐹?
D E
F
Q
S S
201
Week 12 - Keys
Weekly Assessments
202
Week #12 KEY 1. Use the triangles below to answer the
questions that follow.
a) Which side corresponds to ST?
MN
b) Which side corresponds to TU?
𝑀𝑂
2. Identify the fixed points in the following
transformations.
a) A square reflected over its diagonal. All the points on the diagonal b) A rectangle translated to the left by two units. No fixed points
3. Use the diagram below to answer the questions
that follow. C is the midpoint of BD.
a) Which side corresponds to BC? DC b) Show that ∆𝐴𝐵𝐶 ≅ ∆𝐴𝐷𝐶. 𝐴𝐵 ≅ 𝐵𝐶 (Given) AC is shared by the two triangles. Thus 𝐴𝐶 ≅ 𝐴𝐶 C is the midpoint of BD thus 𝐵𝐶 ≅ 𝐷𝐶. Therefore SSS postulate is achieved hence ∆𝐴𝐵𝐶 ≅ 𝐴𝐷𝐶
4. State whether the pairs of triangles are
congruent or not.
a) They are congruent a) They are not congruent
60°
85° 35° S
T
U
60°
M
85°
N
O
A
B
C
D
2.2 𝑖𝑛 2.1 𝑖𝑛
203
5. Identify the postulate making each pair of the
triangles congruent.
a) SAS postulate b) SSS postualate
6. The triangles below are congruent.
a) Which angle corresponds to ∠𝐷? ∠𝑆 b) Which angle corresponds to ∠𝐹?
∠𝑄
D E
F
Q
S S
Day 61 Bellringer
HighSchoolMathTeachers.com©2020 Page 204
1.Identify the rigid motion that can map the pairs of triangles below.
a)
b)
Day 61 Bellringer
HighSchoolMathTeachers.com©2020 Page 205
c)
2. State whether the following statements are true or force.
a) All rigid motions preserves the shape and the size of the figure?
b) Rigid motions changes the angle measure between two adjacent sides of a triangle.
Day 61 Bellringer
HighSchoolMathTeachers.com©2020 Page 206
Answer Key Day 61
1. a) Reflection
b) Glide reflection
c) Translation
2. a) True
b) False
Day 61 Activity
HighSchoolMathTeachers.com©2020 Page 207
1. Draw the diagonals of the plane paper as shown.
2. Label the plane paper as shown below.
3. Cut the rectangle through the diagonals such that you have four triangles.
4. Get ∆𝐾𝐷𝐿 and ∆𝐹𝐸𝐺 and adjust them until they coincide, (if possible).
Is ∆𝐾𝐷𝐿 ≅ ∆𝐹𝐸𝐺?
5. Move ∆𝐴𝐵𝐶 and ∆𝐻𝐼𝐽 and adjust them until they coincide (if possible)
Is ∆𝐴𝐵𝐶 ≅ ∆𝐻𝐼𝐽?
6. Move ∆𝐸𝐹𝐺 and ∆𝐻𝐼𝐽 closer to see if they coincide, (if possible). Is ∆𝐸𝐹𝐺 ≅ ∆𝐻𝐼𝐽?
7. Move ∆𝐾𝐷𝐿 and ∆𝐻𝐼𝐽 closer to see if they coincide, (if possible). Is ∆𝐾𝐷𝐿 ≅ ∆𝐻𝐼𝐽?
8. Among the triangles that are congruent, Identify the transformation that would map one on another
as they appear in their original position in the rectangle.
A B
D E H
I J
F
G
K
L
Day 61 Activity
HighSchoolMathTeachers.com©2020 Page 208
In this activity students will cut different triangles out of a rectangular plane paper and identify
congruent and non-congruent triangles. Students will work in groups of at least three and each group is
required to have a plane paper, a ruler, a pencil and a razor or anything that can cut a piece of paper.
Answer Keys
Day 61:
1-3. No response
4. Yes
5. Yes
6. No
7. No
8. Reflection about a line parallel to the width or the length
Or rotation about the point which is the intersection of the two diagonals of the rectangle
Day 61 Practice
HighSchoolMathTeachers.com©2020 Page 209
Use the graph below to answer questions 1 and 2.
1. Identify a rigid motion that will map ∆𝐴𝐵𝐶𝐷 onto ∆𝐴′𝐵′𝐶′𝐷′.
2. Is ∆𝐴𝐵𝐶𝐷 ≅ ∆𝐴′𝐵′𝐶′𝐷′?
Use the diagram below to answer question 3 and 4.
-6 -4 -2 0 2 4 6 x
y
4
2
-2
-4 A B
C
𝐶′
𝐵′ 𝐴′
D
𝐷′
Day 61 Practice
HighSchoolMathTeachers.com©2020 Page 210
3. Which rigid motion will map the two triangles above?
4. Are the two triangles congruent to each other?
Use the diagram below to answer questions 5 and 6.
5. Identify a rigid motion that will map one triangle onto the other.
6. Are the two triangles congruent to each other?
Use the diagram below to answer questions 7 and 8.
7. Identify a rigid motion that can map the two triangles.
8. Are the two triangles congruent to each other.
Day 61 Practice
HighSchoolMathTeachers.com©2020 Page 211
Study the graph below and use it to answer questions 9 and 10.
9. Identify a rigid motion that can map ∆𝐴𝐵𝐶 onto ∆𝐴′𝐵′𝐶′.
10. Is ∆𝐴𝐵𝐶 ≅ ∆𝐴′𝐵′𝐶′?
Use the diagram below to answer questions 11 and12.
-6 -4 -2 0 2 4 6 x
y
4
2
-2
-4
A B
C 𝐶′
𝐵′ 𝐴′
Day 61 Practice
HighSchoolMathTeachers.com©2020 Page 212
11. Which rigid motion will map one triangles onto the other?
12. Are the two triangles congruent to each other?
Use the diagram below to answer questions 13 and 14.
13. Which rigid motion will map one triangles onto the other?
14. Are the triangles congruent to each other?
Use the graph below to answer questions 15 and 16.
Day 61 Practice
HighSchoolMathTeachers.com©2020 Page 213
15. Which rigid motion will map ∆𝐴𝐵𝐶 to ∆𝑀𝑁𝑂?
16. Is ∆𝐴𝐵𝐶 ≅ ∆𝑀𝑁𝑂
Use the diagram below to answer questions 17 and 18.
17. Which rigid motion will map one triangles onto the other?
18. Are the two triangles congruent to each other?
Use the diagram below to answer questions 19 and 20.
19. Which rigid motion will map one triangles onto the other?
20. Are the two triangles congruent to each other?
Day 61 Practice
HighSchoolMathTeachers.com©2020 Page 214
Answer Keys
Day 61:
1. A rotation of 180° or −180° about the origin.
2. Yes
3. None
4. No
5. Glide reflection
6. Yes
7. Translation
8. Yes
9. Reflection
10. Yes
11. None
12. No
13. Translation
14. Yes
15. A rotation of +90° about the origin
16. Yes
17. Reflection
18. Yes
19. Glide reflection
20. Yes
Day 61 Exit Slip
HighSchoolMathTeachers.com©2020 Page 215
1. Is ∆𝐴𝐵𝐶 ≅ ∆𝑆𝑇𝑈? Explain
A B
C
S T
U
62°
62°
Day 61 Exit Slip
HighSchoolMathTeachers.com©2020 Page 216
Answer Keys
Day 61:
Yes;
The figures are related by glide reflection which a rigid motion
Day 62 Bellringer
HighSchoolMathTeachers.com©2020 Page 217
Given that ΔPQR and ΔXYZ below are congruent, identify the angle or side indicated in each case. Use
the correct correspondence when naming the angles and sides.
(a) PR̅̅̅̅
(b) ∠QPR
(c) YZ̅̅̅̅
(d) ∠YZX
(e) XZ̅̅̅̅
P
Q
R
X
Y
Z
Day 62 Bellringer
HighSchoolMathTeachers.com©2020 Page 218
Answer Keys Day 62:
(a) YZ̅̅̅̅
(b) ∠XYZ
(c) PR̅̅̅̅
(d) ∠PRQ
(e) QR̅̅ ̅̅
Day 62 Activity
HighSchoolMathTeachers.com©2020 Page 219
1. Measure the lengths of 𝐴𝐵̅̅ ̅̅ , 𝐵𝐶̅̅ ̅̅ and 𝐴𝐶̅̅ ̅̅ in inches using a ruler and write down the measurements.
2. Find the measures of ∠𝐴, ∠𝐵 and ∠𝐶 using a protractor and write down these measures.
3. Using a tracing paper and a ruler, carefully duplicate ΔABC and label it ΔKLM in the order shown
below. Are these triangles congruent?
4. Measure the length of KL̅̅̅̅ on ΔKLM using a ruler and write it down. Which side on ΔABC has the
same length as KL̅̅̅̅ ?
A B
C
K L
M
Day 62 Activity
HighSchoolMathTeachers.com©2020 Page 220
5. Measure the length of LM̅̅ ̅̅ on ΔKLM using a ruler and write it down. Which side on ΔABC has the
same length as LM̅̅ ̅̅ ?
6. Similarly, measure the length of KM̅̅̅̅̅ on ΔKLM using a ruler and write it down. Which side on ΔABC
has the same length as KM̅̅̅̅̅?
7. Find the measure of ∠𝐾 in ΔKLM using a protractor and write down its measure. Which angle in
ΔABC has the same measure as ∠𝐾?
8. Find the measure of ∠𝐿 in ΔKLM using a protractor and write down its measure. Which angle in
ΔABC has the same measure as ∠𝐿?
9. Similarly, find the measure of ∠𝑀 in ΔKLM using a protractor and write down its measure. Which
angle in ΔABC has the same measure as ∠𝑀?
Day 62 Activity
HighSchoolMathTeachers.com©2020 Page 221
In this activity students will learn how to identify congruent angles and sides using congruent triangles.
Students will work in groups of two or four and each group will require a tracing paper of A4 size, a ruler
and a protractor. The students in the respective groups will also be provided with a copy of ΔABC shown
below.
Answer keys
Day 62:
1. Lengths should be measured accurately
2. Angles should be measured accurately
3. Yes
4. 𝐴𝐵̅̅ ̅̅
5. 𝐵𝐶̅̅ ̅̅
6. 𝐴𝐶̅̅̅̅
7. ∠𝐴
8. ∠𝐵
9. ∠𝐶
Day 62 Practice
HighSchoolMathTeachers.com©2020 Page 222
Use the figures below to answer questions 1-6.
Given that ΔABC ≅ ΔPQR, identify the parts congruent to the ones indicated in order to show
congruence between the two triangles. Use the correct correspondence in each case.
1. 𝐴𝐶̅̅̅̅
2. ∠𝑄
3. 𝑃𝑄̅̅ ̅̅
4. ∠𝐵
5. 𝐵𝐶̅̅ ̅̅
6. ∠𝑅
A
B
C
P
Q
R
Day 62 Practice
HighSchoolMathTeachers.com©2020 Page 223
Use the figures below to answer questions 7-15.
Triangle KLM is congruent to triangle XYZ.
Identify the parts congruent to the following parts:
7. 𝐾𝐿̅̅̅̅
8. ∠𝑋
9. 𝑋𝑌̅̅ ̅̅
10. ∠𝐿
11. 𝐿𝑀̅̅ ̅̅
12. ∠𝑌
K
L
M
X
Y
Z
62°
70°
48°
Day 62 Practice
HighSchoolMathTeachers.com©2020 Page 224
Find the values represented by the following letters:
13. 𝑥
14. 𝑦
15. 𝑧
Use the triangles to answer questions 16-20.
Δ𝐹𝐺𝐻 and Δ𝐽𝐾𝐿 shown below are congruent. The triangles are not drawn to scale.
Identify parts congruent to the following ones:
16. ∠J
F G
H
J
K
L
4 𝑖𝑛.
2 + 𝑏
8 𝑖𝑛.
2𝑎 − 4
Day 62 Practice
HighSchoolMathTeachers.com©2020 Page 225
17. 𝐹𝐻̅̅ ̅̅
18. ∠K
Hence find the values represented by the letters:
19. 𝑎
20. 𝑏
Day 62 Practice
HighSchoolMathTeachers.com©2020 Page 226
Answer keys
Day 62:
1. 𝑄𝑅̅̅ ̅̅
2. ∠𝐴
3. 𝐵𝐴̅̅ ̅̅
4. ∠𝑃
5. 𝑃𝑅̅̅ ̅̅
6. ∠𝐶
7. 𝑌𝑍̅̅̅̅
8. ∠𝑀
9. 𝑀𝐾̅̅ ̅̅ ̅
10. ∠𝑍
11. 𝑍𝑋̅̅ ̅̅
12. ∠𝐾
13. 𝑥 = 25°
14. 𝑦 = 26°
15. 𝑧 = 5°
16. ∠𝐻
17. 𝐾𝐽̅̅ ̅
18. ∠𝐹
19. 𝑎 = 6
20. 𝑏 = 2
Day 62 Exit Slip
HighSchoolMathTeachers.com©2020 Page 227
In the figure below AB ∥ CD and AB ≅ CD.
Identify the side that is congruent to OC̅̅̅̅ in ΔCOD and ∠ABO in ΔAOB.
A
B
C
D
O
Day 62 Exit Slip
HighSchoolMathTeachers.com©2020 Page 228
Answer Keys
Day 62:
OA̅̅ ̅̅ and ∠CDO
Day 63 Bellringer
HighSchoolMathTeachers.com©2020 Page 229
The diagram below shows a pre-image and its image under a transformation.
1. What is common among lines JT, GU and HV?
2.Identify common features among the two diagrams
3. Identify the transformation mapping one image to another
4. Explain your answer in 3 above.
5. Are the two diagrams congruent? Explain.
J
H
G
T
V
U
Day 63 Bellringer
HighSchoolMathTeachers.com©2020 Page 230
Answer Keys
Day 63:
1. They are parallel and equal
2. Have the same orientation and size
3. Translation
4. Respective image point moves through the same distance and direction
5. Yes, the image is mapped to the object by a translation which is a rigid motion. The fact that
rigid motion preserves distance and angular measurement, the figures are congruent.
Day 63 Activity
HighSchoolMathTeachers.com©2020 Page 231
1. On the graph paper using a suitable scale draw two horizontal lines segments of 3 – 4 units. Let the lie
on one horizontal line of a graph paper.
2. Label the lines as XY and MN respectively.
3. On the right end of each line, draw a vertical line of about 5 – 7 units so that they are vertical to the
lines XY and MN above. Label the endpoints as Z and P so that YZ and NP are perpendicular to XY and
MN respectively.
4. Connect the lines so that we have two triangles XYZ and MNP are two triangles.
5. Measure XZ and MP, compare the measurements.
6. Confirm that the corresponding angles are congruent by first, measuring the corresponding angles
and comparing them.
7. Find the area of each triangle.
8. Compare the size of the triangles, what do you notice.
Day 63 Activity
HighSchoolMathTeachers.com©2020 Page 232
In this activity, we would like to establish that if corresponding angles and sides of a triangle congruent,
then the two triangles are congruent. Student will work in groups of at least 3. Each group will require a
ruler, a pencil, and a graph paper.
Answer Keys Day 63:
1 – 4. No response
5. Different responses. The two measurements should be equal
6. Angle measurements will vary from group to group, however, the corresponding angles must be
approximately equal
7. Different responses but equal area in each group
8. They are congruent
Day 63 Practice
HighSchoolMathTeachers.com©2020 Page 233
Use the following information to answer questions 1 - 8
1. Identify corresponding angles in the above figure
2. Identify corresponding sides in the above figure
3. Find the relationship between the corresponding sides
4. Identify the transformation between the two figures above.
5. Are two figures congruent?
6. Explain your answer 5 above.
7. Having established 5 above, what could be the relationship between the corresponding angles?
8. Explain why the relationship in 7 above.
Q
K
L
Y
X
H
8 in
8 in
6.5 in
6.5 in
4 in
4 in
Day 63 Practice
HighSchoolMathTeachers.com©2020 Page 234
Use the following information to answer the following questions
9. Identify corresponding angles
10. Identify corresponding sides
11. Find the size of angle EDC.
12. Find the size of angle FHG, state the reason for your answer.
13. Find the relationship between the corresponding angles
14. Explain what the answer in 13 suggest.
15. Find the relationships between the corresponding sides.
C
D
E
F
G
H
9.5 in 87°
5.4 in
55°
38°
87°
5.5 in
Day 63 Practice
HighSchoolMathTeachers.com©2020 Page 235
16. Combining the answer in 15 and 13, what is the relationship between the two triangles?
17. Explain your answer in 16 above.
Use the information to answer questions 18 – 20.
Two triangles are related by a dilation of scale factor –1.
18. Are the two triangles congruent?
19. Explain your answer in 18 above.
20. Based on your answer in 18 above, what is the consequences using the theorem
Day 63 Practice
HighSchoolMathTeachers.com©2020 Page 236
Answer keys Day 63:
1. ∠𝐾 and ∠𝐻, ∠𝑄 and ∠𝑌, ∠𝐿 and ∠𝑋.
2. 𝐾𝑄 and 𝑌𝐻, 𝐾𝐿 and 𝐻𝑋, 𝐿𝑄 and 𝑋𝑌
3. 𝐾𝑄 = 𝑌𝐻 = 4 𝑖𝑛, 𝐾𝐿 = 𝐻𝑋 = 6.5 𝑖𝑛 𝐿𝑄 = 𝑋𝑌 = 8 𝑖𝑛
4. Rotation
5. Yes
6. They are mapped onto each other, by rotation, a rigid motion which of course preserves length and
angle measurement, thus, leading to congruent image and pre-image.
7. Corresponding angles are equal
8. From the theorem on congruence, when the two triangles are congruent, their corresponding angles
are too.
9. ∠𝐸 and ∠𝐻, ∠𝐶 and ∠𝐺, ∠𝐷 and ∠𝐹.
10. 𝐶𝐸 and 𝐺𝐻, 𝐸𝐷 and 𝐺𝐹, 𝐷𝐶 and 𝐹𝐻
11. 𝐴𝑛𝑔𝑙𝑒 𝐸𝐷𝐶 = 38°
12. 𝐴𝑛𝑔𝑙𝑒 𝐹𝐻𝐺 = 55°
13. ∠𝐸 = ∠𝐻, ∠𝐶 = ∠𝐺, ∠𝐷 = ∠𝐹.
14. Based on comparison of the angle measures given and those computed
15. No sufficient information given, hence not related but, at least a pair or corresponding angles are
not equal
16. They are not congruent
17. Corresponding angles are equal but corresponding sides are not equal hence, we cannot apply the
theorem on congruence of triangles. Thus, the triangles are not congruent.
18. YES
19. Have a scale factor of absolute one and corresponding angles are equal. This implies that length and
angular measure are maintained.
20. Corresponding sides and angles are equal.
Day 63 Exit Slip
HighSchoolMathTeachers.com©2020 Page 237
Given that the two triangles are congruent, find the relation between their interior angles.
M
N P
S
T
U
5 in
5 in
Day 63 Exit Slip
HighSchoolMathTeachers.com©2020 Page 238
Answer Keys
Day 63:
∠𝑁 = ∠𝑇, ∠𝑃 = ∠𝑈 𝑎𝑛𝑑 ∠𝑀 = ∠𝑆
Day 64 Bellringer
HighSchoolMathTeachers.com©2020 Page 239
1.Identify the postulate that make the following triangles congruent.
a)
b)
c)
Day 64 Bellringer
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2. In the figure below, ∆𝐴𝐵𝐶 is mapped onto ∆𝑀𝑁𝑂 by a reflection. Use the figure to answer the
questions that follow.
a) Which side corresponds to side 𝐴𝐶?
b) Which angle corresponds ∠𝐴𝐵𝐶?
A B M N
C O
Day 64 Bellringer
HighSchoolMathTeachers.com©2020 Page 241
Answer Key
Day 64
1. a) A.S.A postulate
b) S.A.S Postulate
c) S.S.S Postulate
2. a) NO
b) ∠𝑁𝑀𝑂
Day 64 Activity
HighSchoolMathTeachers.com©2020 Page 242
1. Label the square as WXYZ as shown below.
2. Fold the square along the diagonal DB.
3. How many triangles are formed?
4. To they overlap?
5. What is the conclusion about their relation with respect to your answer in 4 above.
6. Is there a transformation relating the two triangles, if yes, which one.
7. Now fold it along AC.
8. Together with the first fold, how many triangles are formed.
9. List the triangles that are congruent to each other given that the diagonals meet at O.
10. What are the postulates used to come up with answers in 9 above
A B
C D
Day 64 Activity
HighSchoolMathTeachers.com©2020 Page 243
In this activity, students will determine the congruent triangles in a square when divided by its
diagonals. They will do so using the postulates. Students will work in groups of at least 3 where each
group will require a square shaped plain paper, a ruler and a pencil.
Answer Keys
Day 64:
1 – 2. No response
3. 2
4. They do
5. They are congruent
6. Reflection along DB
7. No response
8. 8
∆𝐷𝐶𝑂, ∆𝐶𝐵𝑂, ∆𝐵𝐴𝑂 𝑎𝑛𝑑 ∆𝐴𝐷𝑂
∆𝐴𝐵𝐶, ∆𝐴𝐷𝐶, ∆𝐵𝐷𝐴 𝑎𝑛𝑑 ∆𝐵𝐷𝐶
9.SSS or SAS or ASA.
Day 64 Practice
HighSchoolMathTeachers.com©2020 Page 244
Use the diagram below to answer questions 1 - 4.
1. Which postulate show that the triangles are congruent?
2. Find the value of t.
3. Find the value of y
4. Find the value of 𝑥
Use the diagram below to answer questions 5 - 10.
AC and BD are straight lines and point O divides line AC in the ratio 2:1. Line AC is 9𝑖𝑛 long.
5. Which postulate shows that ∆𝐴𝑂𝐷 and ∆𝐶𝑂𝐵 are congruent?
6. Is ∆𝐴𝑂𝐵 ≅ ∆𝐶𝑂𝐷?
7. What is the length of DO?
(2𝑦 + 2)𝑖𝑛
(3𝑥 − 2)𝑖𝑛
(𝑥 + 4)𝑖𝑛
(4𝑦 − 2)𝑖𝑛
(70 + 𝑡)° (3𝑡 − 80)°
O
A B
C D
Day 64 Practice
HighSchoolMathTeachers.com©2020 Page 245
8. What is the length of OB?
9. Is ∆𝐴𝐶𝐷 ≅ 𝐵𝐶𝐷?
10. If yes, which postulate is used in 9 above. If no, Identify the condition that is not met by the
postulate.
Use the rectangle below to answer questions 11 - 13.
11. Which triangle is congruent to ∆𝑆𝑂𝑇?
12. Which triangle is congruent to ∆𝑇𝑂𝑈?
13. Is ∆𝑇𝑂𝑈 ≅ ∆𝑆𝑂𝑇?
Use the figure below to answer questions 14 - 16.
14. Which postulate makes the two triangles congruent?
Day 64 Practice
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15. What is the value of a?
16. What is the value of 𝑥?
17. Find the value of c?
From question 18 - 20, state the postulate which makes each pair of triangles congruent.
18.
19.
20.
Day 64 Practice
HighSchoolMathTeachers.com©2020 Page 247
Answer Key
Day 64:
1. S.A.S
2. 75
3. 2
4. 3
5. S.A.S
6. No
7. 3𝑖𝑛
8. 6𝑖𝑛
9. Yes
10. S.S.S
11. ∆𝑈𝑂𝑉
12. ∆𝑆𝑂𝑉
13. No
14. A.S.A
15. 4 in
16. 35°
17. 53
18. S.S.S
19. S.A.S
20. A.S.A
Day 64 Exit Slip
HighSchoolMathTeachers.com©2020 Page 248
1. Is ∆𝑀𝑁𝑂 ≅ 𝑆𝑇𝑈? Explain
𝑀 𝑁
O
S T
U
Day 64 Exit Slip
HighSchoolMathTeachers.com©2020 Page 249
Answer Keys
Day 64:
1. Yes
The corresponding sides are equal, thus, we have SSS postulate
Unit 4 Test Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 250
Questions:
1. Identify the rigid motion involved in the following transformation.
2. A square of sides 5 cm by 5 cm was translated three units upwards and six units to the right. What
is the area of the image?
3. What is the value of a?
Unit 4 Test Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 251
4. Define a rigid motion!
5. Is this kind of transformation a rigid motion or not? Why?
6. Describe a single rigid motion which can map ∆𝐴𝐵𝐶 to its image.
Unit 4 Test Name ____________________________________
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7. Identify the congruent sides.
8. Which type of rigid motion has mapped ΔPQR onto ΔXYZ?
Unit 4 Test Name ____________________________________
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9. ΔPQR has been mapped onto ΔABC after a half turn about the origin (0,0). Considering ΔPQR and
ΔABC, identify all the pair of congruent angles.
10. State whether each of the following pairs of triangles is congruent or not.
a)
Unit 4 Test Name ____________________________________
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b)
11. Find the value of x if these two triangles are congruent.
12. ∆𝐴𝐵′𝐶′ is an image of ∆𝐴𝐵𝐶. Find the center of dilation.
Unit 4 Test Name ____________________________________
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13. The triangle is dilated about point P with a scale factor of -1. Indicate the image.
14. PQ ≅ PR and PT bisects QR. Show that the two triangles are congruent.
15. Find the third angle of a triangle whose first two angles are 33° and 67°.
16. Find the measure of angle A.
Unit 4 Test Name ____________________________________
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17. State the congruence postulate that makes the following triangles congruent.
18. Define:
a) Congruent angles
b) Congruent sides
19. The diagram shows a pre-image and its image under a transformation. What is common among
lines JT, GU and HV?
Unit 4 Test Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 257
20. Is ∆𝑀𝑁𝑂 ≅ ∆𝑆𝑇𝑈? Why?
Unit 4 Test Name ____________________________________
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Answers:
1. Translation
2. 25 𝑐𝑚2
3. 67°
4. A rigid motion is a transformation on a plane that preserves the distance between the points and
the relative position of the points. There are four rigid motions namely reflection, glide reflection,
translation and rotation.
5. It is not a rigid motion because the size has changed after the transformation.
6. A rotation of 180° about the point (0, 1).
7. YX and QS, XL and SE, and YL and QE
8. Reflection
9.
∠P ≅ ∠A
∠Q ≅ ∠C
∠R ≅ ∠B
10.
a) No
b) Yes
11. x=2 in
12. Point A
13.
14.
Unit 4 Test Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 259
15. 80°
16. 30 degrees
17. ASA postulate
18.
a) Congruent angles that have the same measure.
b) Congruent sides are sides that have the same length.
19. They are parallel and equal.
20. Yes. The corresponding sides are equal, thus, we have SSS postulate.