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Complete Unit 3

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Table of Contents

Unit 3 Pacing Chart -------------------------------------------------------------------------------------------- 1

Geometry Unit 3 Skills List ---------------------------------------------------------------------------------------- 5

Unit 3 Lesson Plans -------------------------------------------------------------------------------------------- 6

Day 31 Bellringer -------------------------------------------------------------------------------------------- 33

Day 31 Activity -------------------------------------------------------------------------------------------- 36

Day 31 Practice -------------------------------------------------------------------------------------------- 39

Day 31 Exit Slip -------------------------------------------------------------------------------------------- 44

Day 32 Bellringer -------------------------------------------------------------------------------------------- 46

Day 32 Activity -------------------------------------------------------------------------------------------- 48

Day 32 Practice -------------------------------------------------------------------------------------------- 51

Day 32 Exit Slip -------------------------------------------------------------------------------------------- 55

Day 33 Bellringer -------------------------------------------------------------------------------------------- 57

Day 33 Activity -------------------------------------------------------------------------------------------- 59

Day 33 Practice -------------------------------------------------------------------------------------------- 62

Day 33 Exit Slip -------------------------------------------------------------------------------------------- 66

Day 34 Bellringer -------------------------------------------------------------------------------------------- 68

Day 34 Activity -------------------------------------------------------------------------------------------- 70

Day 34 Practice -------------------------------------------------------------------------------------------- 72

Day 34 Exit Slip -------------------------------------------------------------------------------------------- 76

Week 7 Assessment -------------------------------------------------------------------------------------------- 78

Day 36 Bellringer -------------------------------------------------------------------------------------------- 87

Day 36 Activity -------------------------------------------------------------------------------------------- 89

Day 36 Practice -------------------------------------------------------------------------------------------- 91

Day 36 Exit Slip -------------------------------------------------------------------------------------------- 109

Day 37 Bellringer -------------------------------------------------------------------------------------------- 111

Day 37 Activity -------------------------------------------------------------------------------------------- 113

Day 37 Practice -------------------------------------------------------------------------------------------- 116

Day 37 Exit Slip -------------------------------------------------------------------------------------------- 127

Day 38 Bellringer -------------------------------------------------------------------------------------------- 129

Day 38 Activity -------------------------------------------------------------------------------------------- 132

Day 38 Practice -------------------------------------------------------------------------------------------- 134

Day 38 Exit Slip -------------------------------------------------------------------------------------------- 149

Day 39 Bellringer -------------------------------------------------------------------------------------------- 151

Day 39 Activity -------------------------------------------------------------------------------------------- 155

Day 39 Practice -------------------------------------------------------------------------------------------- 157

Day 39 Exit Slip -------------------------------------------------------------------------------------------- 171

Week 8 Assessment -------------------------------------------------------------------------------------------- 173

Day 41 Bellringer -------------------------------------------------------------------------------------------- 182

Day 41 Activity -------------------------------------------------------------------------------------------- 187

Day 41 Practice -------------------------------------------------------------------------------------------- 190

Day 41 Exit Slip -------------------------------------------------------------------------------------------- 210

Day 42 Bellringer -------------------------------------------------------------------------------------------- 213

Day 42 Activity -------------------------------------------------------------------------------------------- 215

Day 42 Practice -------------------------------------------------------------------------------------------- 217

Day 42 Exit Slip -------------------------------------------------------------------------------------------- 227

Day 43 Bellringer -------------------------------------------------------------------------------------------- 229

Day 43 Activity -------------------------------------------------------------------------------------------- 231

Day 43 Practice -------------------------------------------------------------------------------------------- 234

Day 43 Exit Slip -------------------------------------------------------------------------------------------- 255

Day 44 Bellringer -------------------------------------------------------------------------------------------- 257

Day 44 Activity -------------------------------------------------------------------------------------------- 261

Day 44 Practice -------------------------------------------------------------------------------------------- 263

Day 44 Exit Slip -------------------------------------------------------------------------------------------- 281

Week 9 Assessment -------------------------------------------------------------------------------------------- 283

Unit 3 Test -------------------------------------------------------------------------------------------- 290

Unit 3 Pacing Chart

Unit Week Day CCSS Standards Objective I Can Statements

Unit 3 Triangles

Week 7 – Prove Theorems

about Triangles 31

CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include:

measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the

segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the

medians of a triangle meet at a point.

Prove that measures of interior angles of a triangle

sum to 180°

I can prove that measures of interior angles of a triangle sum

to 180°

Unit 3 Triangles

about Triangles 32

Prove that base angles of isosceles triangles are

congruent

I can prove that base angles of isosceles triangles are congruent

Unit 3 Triangles

about Triangles 33

Prove that the medians of a triangle meet at a point.

I can prove that the medians of a triangle meet at a point.

Unit 3 Triangles

about Triangles 34

Summarize the week's topics

I can prove that measures of interior angles of a triangle sum

to 180° I can prove that base angles of

isosceles triangles are congruent I can prove that the medians of a

triangle meet at a point.

Unit 3 Pacing Chart

Unit 3 Triangles

about Triangles 35 Assessment Assessment Assessment

Unit 3 Triangles

Week 8 – Geometric

Constructions 36

CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric

software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing

perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line

parallel to a given line through a point not on the line.

Make formal geometric constructions with a variety

of tools and methods (compass and straightedge,

string, reflective devices, paper folding, dynamic

geometric software, etc.). Copying a segment;

copying an angle; bisecting a segment; bisecting an

angle;

I can copy a segment; an angle; bisecting a segment and bisecting

an angle using variety of tools and methods (compass and

straightedge, string, reflective devices, paper folding, dynamic

geometric software, etc.)

Unit 3 Triangles

Constructions 37

Make formal geometric constructions with a variety

of tools and methods (compass and straightedge,

string, reflective devices, paper folding, dynamic

geometric software, etc.).constructing

perpendicular lines, including the perpendicular bisector of a line segment

I can construct perpendicular

lines, including the perpendicular bisector of a line segment using

variety of tools and methods (compass and straightedge,

string, reflective devices, paper folding, dynamic geometric

software, etc.)

Unit 3 Pacing Chart

Unit 3 Triangles

Constructions 38

Make formal geometric

constructions with a variety of tools and methods

(compass and straightedge, string, reflective devices, paper folding, dynamic

geometric software, etc.). constructing a line parallel to a given line through a

point not on the line.

I can construct a line parallel to a given line through a point not on the line uisng variety of tools and

methods (compass and straightedge, string, reflective

devices, paper folding, dynamic geometric software, etc.)

Unit 3 Triangles

Constructions 39

Summarize- Copying a segment; copying an angle;

bisecting a segment; bisecting an angle;

constructing perpendicular lines, including the

perpendicular bisector of a line segment; and

constructing a line parallel to a given line through a

point not on the line.

I can copy a line segment; an angle; bisect a segment and an

angle I can constructing perpendicular lines, including the perpendicular

bisector of a line segment I can constructing a line parallel to a given line through a point

not on the line.

Unit 3 Triangles

Constructions 40 Assessment Assessment Assessment

Unit 3 Pacing Chart

Unit 3 Triangles

Week 9 – Inscribed and Circumscribed

Circles of a Triangle

41 CCSS.MATH.CONTENT.HSG.CO.D.13

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Construct an equilateral triangle inscribed in a

circle.

I can construct an equilateral triangle inscribed in a circle.

Unit 3 Triangles

Construct an square inscribed in a circle.

I can construct an square inscribed in a circle.

Unit 3 Triangles

Construct a regular hexagon inscribed in a

circle.

I can construct a regular hexagon inscribed in a circle.

Unit 3 Triangles

Sammarize - Construction of a equilateral triangle, a

square, and a regular hexagon inscribed in a

circle

I can construct an equilateral triangle inscribed in a circle.

I can construct an square inscribed in a circle.

I can construct a regular hexagon inscribed in a circle.

Unit 3 Triangles

45 Assessment Assessment Assessment

Geometry Unit 3 Skills List Name ____________________________________

Geometry Unit 3 Skills List

Number Unit CCSS Skill

12 3 HSG.CO.C.10 Prove theorems about triangles

13 3 HSG.CO.D.12 Make formal geometric constructions

14 3 HSG.CO.D.13 Construct inscribed figures

Geometry Unit 3 Lesson Plan Name ____________________________________

Unit: Unit 3 Triangles

Course: Geometry

Topic: Week 7 – Prove Theorems about Triangles

Day: 31

Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

Objective: Prove that measures of interior angles of a triangle sum to 180°

I can statement: I can prove that measures of interior angles of a triangle sum to 180°

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will discover that when the interior angles of a triangle are summed up, they add up to 180°. 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 31 Day 31 Activities Day 31 Practice Day 31 Presentation Day 31 Exit Slip

Accommodations/Special Circumstances:

Technology:

Reflection:

Extra/Additional Resources:

Course: Geometry

Day: 32

Objective: Prove that base angles of isosceles triangles are congruent

I can statement: I can prove that base angles of isosceles triangles are congruent

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will discover that an isosceles triangle has at least two equal sides and consequently its base angles are congruent through simple paper folding and cutting 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.

Technology:

Reflection:

Course: Geometry

Day: 33

Objective: Prove that the medians of a triangle meet at a point.

I can statement: I can prove that the medians of a triangle meet at a point.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. Students are required to draw an equilateral triangle and its medians to study where and how they meet. 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.

Technology:

Reflection:

Course: Geometry

Day: 34

Mathematical Practice: CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

Objective: Summarize the week's topics

I can statement: I can prove that measures of interior angles of a triangle sum to 180° I can prove that base angles of isosceles triangles are congruent I can prove that the medians of a triangle meet at a point.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 5. Students are required to draw an Isosceles triangle then prove that the base angles are equal equal, the sum of interior angles is 180° and the medians intersect at a common point.

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:

Course: Geometry

Day: 35

Common Core State Standard: Assessment

Mathematical Practice: Assessment

Objective: Assessment

I can statement: Assessment

Procedures: Assessment

Materials: Assessment

Technology:

Reflection:

Course: Geometry

Topic: Week 8 – Geometric Constructions

Day: 36

Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics.

Objective: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle;

I can statement: I can copy a segment; an angle; bisecting a segment and bisecting an angle using variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of four to copy a line segment using a straightedge, a ruler, a pencil, a pair of compasses and an A4 size plain paper. 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.

Technology:

Reflection:

Course: Geometry

Day: 37

Objective: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).constructing perpendicular lines, including the perpendicular bisector of a line segment

I can statement: I can construct perpendicular lines, including the perpendicular bisector of a line segment using variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students are required to draw perpendicular lines using a string 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.

Technology:

Reflection:

Course: Geometry

Day: 38

Objective: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). constructing a line parallel to a given line through a point not on the line.

I can statement: I can construct a line parallel to a given line through a point not on the line uisng variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. we would like construct parallel lines using a paper folding technique. 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.

Technology:

Reflection:

Course: Geometry

Day: 39

Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

Objective: Summarize- Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

I can statement: I can copy a line segment; an angle; bisect a segment and an angle I can constructing perpendicular lines, including the perpendicular bisector of a line segment I can constructing a line parallel to a given line through a point not on the line.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. Students are required to construct a perpendicular lines through paper folding. 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.

Technology:

Reflection:

Course: Geometry

Day: 40

Technology:

Reflection:

Course: Geometry

Topic: Week 9 – Inscribed and Circumscribed Circles of a Triangle

Day: 41

Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Objective: Construct an equilateral triangle inscribed in a circle.

I can statement: I can construct an equilateral triangle inscribed in a circle.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. They will draw an equilateral triangle inscribed in a circle using a straightedge and a pair of compasses. 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.

Technology:

Reflection:

Course: Geometry

Day: 42

Objective: Construct an square inscribed in a circle.

I can statement: I can construct an square inscribed in a circle.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. we would construct a square inside a circle using a pairs of compass and a straightedge. 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.

Technology:

Reflection:

Course: Geometry

Day: 43

Objective: Construct a regular hexagon inscribed in a circle.

I can statement: I can construct a regular hexagon inscribed in a circle.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least three to construct a regular polygon inscribed in a circle using paper folding 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.

Technology:

Reflection:

Course: Geometry

Day: 44

Objective: Summarize - Construction of a equilateral triangle, a square, and a regular hexagon inscribed in a circle

I can statement: I can construct an equilateral triangle inscribed in a circle. I can construct an square inscribed in a circle. I can construct a regular hexagon inscribed in a circle.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will construct a square inscribed in a circle 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.

Technology:

Reflection:

Course: Geometry

Day: 45

Technology:

Reflection:

Day 31 Bellringer Name ____________________________________

1. In the figure below lines PQ and RS are parallel. State whether the following angles are corresponding,

alternate interior or alternate exterior angles.

(a) ∠2 and ∠7

(b) ∠3 and ∠7

(c) ∠3 and ∠6

2. Find the alternate interior and alternate exterior angles represented by letters. The two lines shown

in each case are parallel.

𝑥 𝑦

Answer Keys

Day 31:

1. (a) Alternate interior angles

(b) Corresponding angles

(c) Alternate exterior angles

2. (a) 𝑥 = 113°, 𝑦 = 67°

(b) 𝑥 = 31°, 𝑦 = 149°

Day 31 Activity Name ____________________________________

1. On the plain paper provided, draw two straight lines of about 5 inches each on either sides of the

ruler to form a pair of parallel lines as shown below. Label the two lines as PQ and RS as shown below.

2. Mark a point, A, on line PQ at the position shown below.

3. Similarly, mark two points, B and C on line RS in the positions shown below.

4. Now, using a ruler draw two lines, from point A to point C and from point A to point B respectively as

shown below.

5. What name is given to the plane figure formed between points A, B and C?

6. Consider the following angles: ∠BAC, ∠ABC and ∠ACB. Are these angles located within or outside the

plane figure you have identified in 5 above?

7. Measure these three angles accurately using a protractor: ∠BAC, ∠ABC and ∠ACB and write down

their measures.

8. What is the sum of these three angles? Do you think this is usually the case for any plane figure of the

same kind?

In this activity students will work in groups of four to discover that when the interior angles of a triangle

are summed up, they add up to 180°. Students in the respective groups will require a pencil, a plain

paper, a ruler and a protractor. It is assumed from the foregoing that students are comfortable with

measuring angles using a protractor.

Answer Keys

Day 31:

1. No response

2. No response

3. No response

4. No response

5. Triangle

6. Located within the plane figure

7. Each of the three angles will vary from group to group depending on the triangle they have come up

8. The sum should be accurately 180°. This is a question to enable the students think of any other

triangle having interior angles summing up to 180° though most of them will agree.

Day 31 Practice Name ____________________________________

Use the figure below to answer question 1-5. RS ∥ PQ and the two transversal lines intersect the pair of

parallel lines to form triangle ABC as shown below.

1. Find the measure of ∠𝑦

2. Find the measure of ∠𝑧

3. Find the measure of ∠𝑥

4. Find the sum of ∠𝑥, ∠𝑦 and ∠𝑧.

5. What is your conclusion about the sum in question 4 in relation to the triangle formed above?

B C 44°

Use the figure below to answer questions 6-13. Triangle PQR is formed between the parallel lines.

6. Find the measure of ∠𝑦

7. Find the measure of ∠CQP

8. Find the measure of ∠BPQ

9. Find the measure of ∠BPR

10. Find the measure of ∠𝑧

11. Find the measure of ∠𝑥

12. Find the sum of the interior angles ∠𝑥, ∠𝑦 and ∠𝑧 in the figure above.

Q C R 81°

13. What do you discover about the sum in question 12 with respect to the triangle formed above?

Use the figure below to answer questions 14-20. FG ∥ HI and the two transversal lines intersect the pair

of parallel lines to form triangle XYZ.

14. Find the measure of ∠FXY

15. Find the measure of ∠FXZ

16. Find the measure of ∠𝑏

17. Find the measure of ∠𝑎

18. Find the measure of ∠𝑐

19. Find the sum of these angles: ∠𝑎, ∠𝑏 and ∠𝑐

20. What does this tell you about the three angles in relation to triangle XYZ?

Answer keys

Day 31:

1. ∠𝑦 = 44°

2. ∠𝑧 = 59°

3. ∠𝑥 = 77°

4. 180°

5. The sum of interior angles of the triangle add up to 180°

6.∠𝑦 = 81°

7. 99°

8. 99°

9. 29°

10. ∠𝑧 = 29°

11. ∠𝑥 = 70°

12.180°

14. 69°

15. 152°

16. ∠𝑏 = 69°

17. ∠𝑎 = 83°

18. ∠𝑐 = 28°

19. 180°

Day 31 Exit Slip Name ____________________________________

In the figure below, AB ∥ CD and the two transversal lines intersect the pair of parallel lines to form

triangle JKL as shown below.

(a) Find the measure of ∠𝑎

(b) Find the measure of ∠𝑏

(c) Find the measure of ∠𝑐

(d) Find the sum of ∠𝑎, ∠𝑏 and ∠𝑐. What is your conclusion about that sum in relation to the triangle

formed above?

Answer Keys

Day 31:

(a) ∠𝑎 = 62°

(b) ∠𝑏 = 47°

(c) ∠𝑐 = 71°

(d) ∠𝑎 + ∠𝑏 + ∠𝑐 = 62° + 47° + 71° = 180°.

The interior angles of the triangle add up 180°

In the figure below, triangle PQR is formed between the pair of parallel lines AB and CD.

(a) Find the measure of ∠𝑦

(b) Find the measure of ∠BPR

(c) Find the measure of ∠𝑥

(d) Find the measure of ∠𝑧

(e) Compare the measure of ∠𝑥 to that of ∠𝑦, is there any relationship between the two angles?

Q C R 79°

Answer Key Day 32:

(a) ∠𝑦 = 79°

(b) ∠𝐵𝑃𝑅 = 22°

(c) ∠𝑥 = 79°

(d) ∠𝑧 = 22°

(e)∠𝑥 = ∠𝑦 = 79° ; They are congruent.

1. Label the plain paper provided as ABCD.

2. Fold the paper carefully at its center making sure the edge AB is aligned exactly on the edge CD as

shown below.

3. Using the pair of scissors provided, cut carefully the folded paper along the diagonal as shown below.

4. Remove the outer cut-out and open up the paper as shown below. What type of plane figure is

formed from the other cut-out?

5. Label the remaining vertex as P.

6. Using a ruler, measure 𝐵𝑃̅̅ ̅̅ and 𝐷𝑃̅̅ ̅̅ in inches on the cut out. What do you notice?

7. Using a protractor, measure angles ∠BDP and ∠DBP and compare their measures. What do you

notice?

In this activity the students will work in groups of four to discover that an isosceles triangle has at least

two equal sides and consequently its base angles are congruent through simple paper folding and

cutting. The students in the respective groups will require an A5 size plain paper, a protractor, a pair of

scissors and a ruler. Emphasize that each procedure to be done carefully to guarantee accurate

observations.

Answer Keys Day 32:

1. No response

2. This is to ensure that the fold is straight and it connects the midpoint of edge AC to midpoint of edge

3. No response

4. Triangle

5. No response

6. 𝐵𝑃̅̅ ̅̅ = 𝐷𝑃̅̅ ̅̅

7. ∠BDP = ∠DBP

Use the figure below to answer questions 1-5.

Isosceles triangle ABC is formed by the parallel lines XY and PQ. ∠CAY = ∠ABC = 𝜃.

1. Find the measure of ∠BAX in terms of 𝜃.

2. Find the measure of ∠ACB in terms of 𝜃.

3. Find the measure of ∠BAC in terms of 𝜃.

4. Express the sum of angles ∠ABC, ∠ACB and ∠BAC.

5. Compare the measures of ∠ABC to ∠ACB. What do you notice?

Use the figure below to answer questions 6-11. The parallel lines JK and LM together with the two

transversal lines form triangle PQR as shown below. ∠JPQ = ∠KPR = 𝛼.

6. Find the measure of ∠QPR in terms of 𝛼.

7. Find the measure of ∠PQR in terms of 𝛼.

8. Find the measure of ∠PRQ in terms of 𝛼.

9. Identify two congruent interior angles in triangle PQR.

10. Hence, identify two equal edges on triangle PQR.

11. Using your responses from questions 9 and 10, give the type of triangle PQR.

Use the figure below to answer questions 12-16. Triangle XYZ is formed between the parallel lines FG

and JK. ∠MXF = ∠GXN = β.

12. Find the measure of ∠MXN in terms of 𝛽.

13. Hence, find the measure of ∠YXZ in terms of 𝛽.

13. Find the measure of ∠FXY in terms of 𝛽.

14. Find the measure of ∠GXZ in terms of 𝛽.

15. Using the measure of ∠MXF, find the measure of ∠XZY.

16. Using the measure of ∠GXN, find the measure of ∠XYZ.

17. Compare ∠XZY to ∠XYZ. What is the relationship between the two angles?

18. Using the relationship between angles ∠XZY and ∠XYZ, identify two equal line segments from

triangle XYZ above.

19. Using information from questions 17 and 18 above, what type of triangle is triangle XYZ?

20. Give the major reason to support your response to question 19 above.

Answer keys Day 32:

1. 𝜃

2. 𝜃

3. 180° − 2 𝜃

4. 180°

5. ∠ABC = ∠ACB = θ; The two angles are congruent.

6. 180° − 2𝛼

7. 𝛼

8. 𝛼

9. ∠PQR and ∠PRQ

10. PQ̅̅̅̅ and PR̅̅̅̅

11. Isosceles

12. 180° − 2𝛽

13. 180° − 2𝛽

14. 𝛽

15. 𝛽

16. 𝛽

17.∠XZY = ∠XYZ; The two angles are congruent

18. XY̅̅̅̅ and XZ̅̅̅̅

19. Isosceles

20 The base angles are equal; ∠XZY = ∠XYZ

In the figure below isosceles triangle JKL is formed between the parallel lines AB and CD. ∠AJK =

∠AJM = β.

(a) Find the measure of ∠JKL in terms of 𝛽.

(b) Find the measure of ∠JLK in terms of 𝛽.

(c) Compare the measures of angles ∠JKL and ∠JLK. What do you discover?

Answer Keys

Day 32:

(a) ∠JKL = β

(b) ∠JLK = β

(c) ∠JKL = ∠JLK = β ; The two angles are congruent.

1. ABC is an isosceles triangle. Line AB = 3 inches and line AC = 5 inches. Use the triangle to answer the

questions that follow.

a) Find the length of AD.

b) What is the length of BD?

c) Find the length of the side BC

d) If ∠𝐶𝐴𝐷 = 31°, What is the size of ∠𝐶𝐵𝐷

2. A line DF is 9 inches long. If G is its midpoint, find the size of line GF.

Answer Key Day 4

1. a) 1 ∙ 5 𝑖𝑛𝑐ℎ𝑒𝑠

b) 1 ∙ 5 𝑖𝑛𝑐ℎ𝑒𝑠

c) 5 𝑖𝑛𝑐ℎ𝑒𝑠

d) 31°

2. 4 ∙ 5 𝑖𝑛𝑐ℎ𝑒𝑠

1. Draw a line of length 4 inches and name it AB.

2. Place the protractor on line AB as shown the measure angle60°.

4. Remove the protractor and join point A and the mark with a straight line as shown below.

5. Measure a distance of 4 inches along the line you have drawn in 4 above, mark it and label it C as

shown.

6. Using a pencil and a ruler, join C and B with a straight line to get ∆𝐴𝐵𝐶 below

7. Mark the midpoints of sides AB, AC and BC as D, E and F respectively.

8. Join the ∠𝐴 and F, ∠𝐶 and D then ∠𝐵 and E as shown below.

What do you notice about the intersection of the midpoints?

In this activity, students are required to draw an equilateral triangle and its medians to study where and

how they meet. Students are required to work in groups of at least three. Each group is required to have

a plane paper, a pencil, a protractor and a ruler.

Answer Keys Day 33:

1-7. No response

8. They all meet at the same point

Use the information below to answer questions 1 - 5.

In ∆𝑆𝑇𝑅, 𝑆𝑇 = 11 𝑖𝑛𝑐ℎ𝑒𝑠, 𝑇𝑅 = 8 𝑖𝑛𝑐ℎ𝑒𝑠 𝑎𝑛𝑑 𝑅𝑆 = 10 𝑖𝑛𝑐ℎ𝑒𝑠. The line segments AT, CR and BS are

the medians of ∆𝑆𝑇𝑅.

1. What is the length of BR?

2. Find the length of SC

3. What is the length of AR?

4. What is the length of AS?

5. Find the length of BT.

In questions 6 to 10. State whether the given statement is true or false.

6. A midpoint of a line divides it into two equal parts.

7. Medians of a triangle meet at two different points.

8. Medians of a triangle meet at one of its vertices.

9. Median of a triangle must run from one vertex and meet the opposite side at a right angle.

10. Medians of a triangle meet at one point.

11. Draw the medians of the triangle given below.

Use the triangle below to answer questions 12 – 17

The Line segments AN, MB and CO are the medians of ∠𝑀𝑁𝑂.

12. Write an equation that relates AM and AF.

13. Write an equation that can relate AM and FM.

14. If FB is 3 ∙ 5 𝑖𝑛𝑐ℎ𝑒𝑠 long. What is the length of the side FN.

15. Write an equation that relates MC and CN.

16.Write an equation that relates MC and MN.

17. Which name is given to the point marked F?

Use the triangle below to state whether the statements given questions 18 – 20 is true or false.

CF, BD and AE are the medians of the triangle.

18. AB =1

2𝐴𝐹

19. ∠𝐶𝐷𝑂 𝑚𝑢𝑠𝑡 𝑏𝑒 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 90°

20. CE ≠ EB

Answer Key

Day 33

1. 4 inches

2. 5 ∙ 5 𝑖𝑛𝑐ℎ𝑒𝑠

3. 5 inches

4. 5 inches

5. 4 inches

6. True

7. False

8. False

9. False

10. True

12. AM = AF

13. FM = 2AM

14. 7 Inches

15. MC = CN

16. MN = 2MN

17. Centroid

18. False

19. False

20. False

1. Draw the medians of the following triangle identifying any resultant features created as a result of

drawing the medians.

Answer Keys

Day 33:

1. If a triangle is symmetrical about = 𝑥 , is their any rigit motion that can be realized in any form of

setup created by the triangle. Which one, explain.

2. One of the base angles of an Isosceles triangle is 40°, find the size of all other angles.

3. Can we have a base angle of an Isosceles triangle being 90°? Explain your answer.

4. Explain why one can view an equilateral triangle as an Isosceles triangle.

5. Two triangles with a common side have two corresponding vertices at equal distance from the

common side. What is the condition that such kind of set up will make a bigger triangle when the

common side is deleted?

Answer Key

Day 34

1. Yes, reflection. One sid of the triangle below 𝑦 = 𝑥 is a reflection of the one above it or vise

versa.

2. 40° and 100°

3. No because the sum of the two base angles would be 180° before the third one is added. This

cannot be since the sum of all interior angles must be 180°.

4. An equilateral triangle has at least two equal angles and sides.

5. The two corresponding vertices must be on the same line as one of the ends of the common

1. On a plane paper, draw a straight line of length between 2 and 4 inches.

2. From one side of the drawn line, draw another line of the same length to meet at an acute angle

4. Connect the ends of the two lines to form a triangle.

5. Confirm that the triangle formed in an Isosceles triangle by measuring and writing their lengths.

6. Label the vertices.

7. Identify the base line and the base angles.

8. Measure the all interior angles.

9. Sum the angles and what do you get?

10. What is common about the measurements of the base angles?

11. Draw the medians of the lines, what do you notice?

In this activity, students are required to draw an Isosceles triangle then prove that the base angles are

equal, the sum of interior angles is 180° and the medians intersect at a common point. Students will

work in groups of 5. Each group will be provided with a plane paper, a pencil, a ruler and a protractor.

Answer Keys Day 34:

1 – 4. No response

5. Answers will vary but two must sides must be approximately equal

6. No response

7 - 8. Answers may vary

9. 180°

10. They are equal

11. They intersect at the same point

In the figure below, lines HE and AD are parallel. Angle 𝐹𝐺𝐸 = 61° and angle 𝐹𝐺𝐶 = 97°.

1. Find the size of angle EGC

2. Find the size of angle GCB

3. Find the size of angle HGB

4. Find the size of angle ABG

5. Find the size of angle GBC

6. Find the size of angle BGC

7. Find the sum of angles GBC, BCG and CGB.

A B C D

Consider the following triangle.

8. Identify the type of triangle.

9. Identify the points in each line that divides it into two equal parts.

10. Draw all the medians of the triangle.

11. Identify the number of points where they meet.

12.Identify if the point(s) above are inside or outside the triangle.

In the figure below, line 𝑀𝐿 = 𝐾𝐿 and 𝑀𝑁 = 𝑁𝐾. KM = 24 in and ML = 20 in and angle 𝑀𝐿𝑁 = 37°.

13. Find the size of line NK.

14. Find the size of line KL.

15. Identify any two pairs of complementary angles.

16. Find the size of angle KLN.

17. Find the size of angle NKL

18. Find the size of angle NML

19. Compare the size of angles in 17 and 18 above.

20. Identify, if any, a rigid motion between triangles MNL and NKL.

Answer Key

Day 34

1. 36°

2. 36°

3. 61°

4. 119°

5. 61°

6. 83°

7. 180°

8. Scalene Triangle

9. Answers may vary

11. One

12. Inside

13. 12 in

14. 20 in

15. Angles NML and MLN

Angles NLK and LKN

16. 37°

17. 53°

18. 53°

19. The angles are equal to 53°

20. Reflection

A triangle is symmetrical about 𝑥 −axis. Identify the 𝑦 −codinate of the point at which the medians

meet. Explain why.

Answer Keys

Day 34:

The 𝑦 −coordinate is 0.

This is because one of the medians will lie of the 𝑥 −axis whose equation is 𝑦 = 0. Since the point of

intersection is shared among all the medians, it must satisfy the equation of each median including 𝑦 =

0, thus, the 𝑦 coordinate.

High School Math Teachers

Geometry

Weekly Assessment Package

Week 7

Weekly Assessments

Week #7 1. Use the figure below to answer the questions that follow.

a) By supplementary angles property, find the size of ∠𝐵𝐶𝐸 . b) By alternate angles property, find the size of ∠𝐵𝐸𝐶. c) By alternate angles property, find the size of ∠𝐶𝐵𝐸. d) Find ∠𝐵𝐸𝐶 + ∠𝐵𝐶𝐸 + ∠𝐶𝐵𝐸

2. The triangle below is reflected through side

a) On the figure, draw the image.

b) What is the size of ∠𝐴𝐴′𝐶?

3. Use the triangle below to answer the

questions that follow.

a) Find the value of 𝑥.

b) Find the size of each base angle.

4. Line AB passes through points 𝐴(3, −2) and

𝐵(8,0). Line BC is perpendicular to AB.

a) Find the slope of BC.

b) Find the equation of BC.

5. Lines CD and EF are parallel. Line

CD passes through points 𝐶(4,6) and

𝐷(13,4). Line EF passes through

point 𝐹(5,1).

a) Find the slope of EF.

b) Find the equation of EF.

56° (2𝑥 + 20)° ( 4𝑥 )°

6. Use the figure below to answer the questions

that follow.

a) Find the size of angle 𝑎.

b) Find the size of angle 𝑏.

Week 7 - KEYS

Weekly Assessments

Week #7 KEY

1. Use the figure below to answer the questions that follow. a) By supplementary angles property, find the size of ∠𝐵𝐶𝐸 . 67° b) By alternate angles property, find the size of ∠𝐵𝐸𝐶. 58° c) By alternate angles property, find the size of ∠𝐶𝐵𝐸. 55° d) Find ∠𝐵𝐸𝐶 + ∠𝐵𝐶𝐸 + ∠𝐶𝐵𝐸

2. The triangle below is reflected through side BC.

c) On the figure, draw the image.

d) What is the size of ∠𝐴𝐴′𝐶?

3. Use the triangle below to answer the questions that follow.

c) Find the value of 𝑥.

d) Find the size of each base angle.

Each base is equal to 40°

4. Line AB passes through points 𝐴(3, −2) and 𝐵(8,0). Line BC is perpendicular to AB.

c) Find the slope of BC.

d) Find the equation of BC.

2𝑦 = −5𝑥 + 15

5. Lines CD and EF are parallel. Line CD passes through points 𝐶(4,6) and 𝐷(13,4). Line EF passes through point 𝐹(5,1).

c) Find the slope of EF.

d) Find the equation of EF.

𝑦 = −2

9𝑥 +

(2𝑥 + 20)° ( 4𝑥 )°

56° 𝐴′

6. Use the figure below to answer the questions that follow.

c) Find the size of angle 𝑎.

d) Find the size of angle 𝑏.

1. Briefly describe the meaning of the following terms in your own words as used in geometry:

(a) Line segment

(b) Angle

(c) Ray

2. Sketch a diagram to show the following:

(a) End points of a line segment

(b) Perpendicular lines

Answer Keys

Day 36:

NB: Target the key words in the description of the terms

1. (a) A portion/part of a line between two endpoints

(b) The amount of turn/ space between two rays diverging from a common point or meeting

at a common point.

(c) A line having one endpoint and extending infinitely in the other direction.

2. (a)

The symbol for parallel lines must be shown.

Endpoint Endpoint

1. Draw a straight line segment of exactly three inches using the straightedge.

2. Label the line segment PQ as shown below.

3. Ensuring that the straightedge is aligned on segment PQ at the upper edge, draw another line

segment below PQ as shown below. It should be slightly longer than PQ.

4. Label point R on the new line segment as shown above.

5. Using the pair of compasses and taking point P as the center and radius PQ, carefully take the length

of PQ.

6. Using the same radius and now using R as the new center, make a mark on the new line segment.

Label the new point S as shown below.

7. What type of lines are PQ and RS?

8. Using a ruler measure the length of segment RS in inches.

9. Compare the lengths of RS to the length of PQ. What do you discover?

10. Is it correct to say that segment RS is a copy of segment PQ? Give a reason.

In this activity students will work in groups of four to copy a line segment using a straightedge, a ruler, a

pencil, a pair of compasses and an A4 size plain paper.

Answer Keys Day 36:

1. No response

2. No response

3. This is to ensure that PQ ∥ RS

4. No response

5. No response

6. No response

7. Parallel lines

8. RS = 3 in.

9. PQ̅̅̅̅ = RS̅̅̅̅

10. Yes, they two segments have the same length and they are parallel as well

Bisect the line segments in questions 1-5. In each case use a straightedge and a pair of compasses only.

Bisect accurately the angles in questions 6-10 using a straightedge and a pair of compasses only. Label

the duplicate angles using suitable letters.

Copy accurately the line segments in questions 11-15 to a different position using a straightedge and a

pair of compasses only. Label the duplicate segments using any appropriate letters.

Copy accurately the angles in questions 16-20 to a different position using a straightedge and a pair of

compasses only.

Answer keys

Day 36:

AM̅̅̅̅̅ = MB̅̅ ̅̅

PM̅̅ ̅̅ = MQ̅̅̅̅̅

KM̅̅̅̅̅ = ML̅̅ ̅̅

MO̅̅̅̅̅ = ON̅̅ ̅̅

RM̅̅̅̅̅ = MS̅̅ ̅̅

Copy ∠KLM below using a straightedge and a compass only. Name the duplicate angle ∠PQR.

Answer Keys

Day 36:

The accuracy of the measure of ∠PQR should be ascertained; ∠KLM ≅ ∠PQR

1. Given that C is the midpoint of line AB and that the length of AC is 3𝑥, what is the leghth of the line

2. Construct a perpendicular bisector to the line given below.

3. State whether the following statements are true or false.

a) A bisector of a line is also perpendicular to the line.

b) When constructing a line bisector, we should change the radius of the compass after drawing each

c) A bisector of a line passes through its midpoint.

A 3𝑥 C B

Answer Key Day 37

1. 6𝑥

3. a) True

b) False

c) True

1. Draw a 3 in straight line on a plain paper and label it AB.

2. Tie one end of the string to the pencil(make sure the string is tied close to the tip of the pencil)

3. Tie the other end of the string to a push pin and let the pushpin be held right at point A. Ensure the

length of the string between the push pin and the pensil is less than that of AB and more than half AB.

4. With the string fully stretched, draw a circle around point A as shown below.

5. Remove the string from point A and hold it on point B.

6. Draw another circle around point B as shown below.

7. Label the points of intersection of the two circles as C and D and join them with a straight line as

shown below.

8. Measure the angle of intersection of the lines AB and CD. What the value?

In this activity students are required to draw perpendicular lines using a string. Students will work in

groups of at least four and each group is required to have a string (which is more than 6 inches long ), a

pencil, a plain paper, a protractor, push pin and a straightedge.

Answer Keys

Day 37:

1-7. No response

8. 𝐴𝑏𝑜𝑢𝑡 90°

Study the figure below and use it to answer questions 1 and 2.

1. Which construction tool might have been used to construct the line perpendicular to AB?

2. Is AB always perpendicular to ST.

3. When you are required to draw a line perpendicular to the given line at O, one is required ti draw an

arc or a circle as the first step. Therefore, draw a suitable circle as your first step in the process.

4. Construct a line perpendicular to the line MN using a compass and a straight edge

5. State whether the following statement is true or false.

A perpendicular line always divides a line into two equal parts.

From question 6 to 12 construct a line which is perpendicular to the given line.(Leave all the marks)

13. Use a straightedge and a compass to construct a line passing through point O and perpendicular to

line given below.

14. A student constructed two perpendicular lines below using a certain construction tool. Which

combination of construction tool was used if the student left all the marks.

15. The diagram below shows a construction of a line perpendicular to line KL. Complete the

construction.

16. Make the first two arcs you would make to construct a line perpendicular to line AB through point C.

17. Below is a diagram showing uncompleted construction of a line perpendicular to line MN through

point C. Using a compass and a straightedge, complete the construction.

18. The diagram below shows uncompleted construction of a line perpendicular to line AB through point

O. Use a compass and the straightedge to complete the construction.

In questions 19 and 20, use a string and a straightedge to construct a line perpendicular to the given line

segment.

Answer Key Day 37

1. Compass and straightedge.

2. Yes

5. False

14. Reflective device and a straightedge

1. Using a compass and a straightedge construct a line which is perpendicular to line AB.

Answer Keys

Day 37:

1. Transfer the following angles to the given points

(iii).

2. Transfer the following points to the given locations

Answer Key Day 38

1. (i).

(iii).

2. (i)

1. On the A4 plain paper, draw a horizontal line of between 4 to 6 inches.

2. Draw a line to intersect the horizontal one at acute angle at point A, about 1.5 in from the left hand

end of the horizontal line.

3. Label point B on the horizontal line about 2.5 to 3 inches from A. Label one side of the intersecting

line so that the acute angle in 2 above is angle DAB.

4. Place the fairly transparent paper to cover point A. Then trace lines AB and AD using a straight line.

5. Fold the paper along those lines drawn so that it forms an angle each to that of angle DAB with the

vertex A consciously visible.

6. Put the folded angle with the position of the vertex at B and one side of the folded angle lying along

the extension of the segment AB.

7. Draw a straight line of the other side of the folded angle. Label the side above BA as C

8. Measure angles DAB and CBA

9. Find the sum of the angles above. What do you deduce from the relation about line DA and BC

In this activity, we would like construct parallel lines using a paper folding technique. Students will work

in groups of 4. Each group will require a one A4 plain paper and another fairly transparent paper, a

pencil, protractor and a straight angle

Answer Keys

Day 38:

1 – 7.No response

8. Difference responses

9. They are parallel

Use the following information to answer questions 1 - 3.

Transfer the angle at the given points.

Draw lines parallel to the one given to pass through A using a set square.

Use the following information to answer questions 13 – 18

Use angle transfer method to draw a parallel line to AC to pass through P.

Use parallelogram method in question 19 and 20 to construct a line parallel to TS through point G.

Answer Keys

Day 38:

List at least three methods of drawing parallel lines

Answer Keys

Day 38

Use of

(i). Reflecting devised

(ii). Strings and pins

(iii). Set squares

(iv). Angle transfer method (compass and a straightedge)

(v). Parallelogram method (compass and a straightedge)

1. Copy line segment given below using a compass and a straightedge.

2. Use a compass and a straightedge to complete the construction of an angle bisector to ∠𝐴𝑂𝐶 below.

3. Construct a perpendicular bisector to the line segment given below.

4. The diagram below shows partly completed construction of a line perpendicular to line AB through

point C. Complete the construction.

5. Draw a perpendicular line to AB through point O.

Answer Key

Day 39

1. Draw a straight line of length 3in at the center of semi-transparent plane paper.

2. Label the line as AB.

3. Fold the paper the paper across line AB so that the end A of the line overlaps with the end B.

4. Press the folded paper firmly to make a crease.

5. Unfold the paper and draw a line through the creases.

6. Measure the angle of intersection of the two lines. What do you get as the angle of intersection.

In this activity students are required to construct a perpendicular lines through paper folding. Students

will work in groups of at least three. Each group is required to have a straightedge or a ruler, a pencil,

and a semi-transparent plane paper.

Answer Keys

Day 39:

1-5. No response

6. About 90°

In questions 1 and 2, copy the given line segments.

3. Copy the angle given below.

4. Bisect the angle given below.

5. Bisect the angle given below.

In questions 6 to 9, construct a perpendicular bisector to the given line segment

In questions 10 to 13 construct a line perpendicular to the given line. (leave all the construction marks)

14. Construct a perpendicular bisector to the line segment given below.

In questions 15 to 20, construct a line parallel to the given line that is passing through point marked P.

Answer Key

Day 39

1. Bisect ∠𝑀𝑂𝑁 below.

Answer Keys

Day 39:

Geometry

Week 8

Weekly Assessments

Week #8 1. Copy the line segment and the angle below.

Show all the marks

2. Construct a line bisector to the line segment and the

angle below. Show all the marks

3. Construct lines perpendicular the following lines. Show all the marks.

4. Use the figure below to answer the questions

that follow.

a) Use the property of supplementary angles to

find the size of ∠𝑋𝑇𝑌.

b) What is the size of ∠𝑌𝑋𝑇?

c) What is the size of ∠𝑋𝑌𝑇?

d) Solve ∠𝑋𝑇𝑌 + ∠𝑌𝑋𝑇 + ∠𝑋𝑌𝑇

5. The triangle below is reflected through side

a) Where will ∠𝑆 match?

b) Where will ∠𝑆𝑉𝑈 match?

c) Is ∠𝑆 = ∠𝑇?

a) Find the value 𝑥.

b) Find the size of ∠𝐴.

71° 60°

(2𝑥)°

(𝑥 + 15)° (3𝑥 − 15)° A B

Week 8 - KEYS

Weekly Assessments

Week #8 KEY 1. Copy the line segment and the angle below. Show all the marks

2. 3Construct a line bisector to the line segment and the angle below. Show all the marks

3. Construct lines perpendicular the following lines. Show all the marks.

e) Use the property of supplementary angles to

find the size of ∠𝑋𝑇𝑌.

49° f) What is the size of ∠𝑌𝑋𝑇?

71° g) What is the size of ∠𝑋𝑌𝑇?

60° h) Solve ∠𝑋𝑇𝑌 + ∠𝑌𝑋𝑇 + ∠𝑋𝑌𝑇

5. The triangle below is reflected through side UV.

d) Where will ∠𝑆 match?

Onto ∠𝑇

e) Where will ∠𝑆𝑉𝑈 match?

Onto ∠𝑇𝑈𝑉

f) Is ∠𝑆 = ∠𝑇?

Yes 6. Use the figure below to answer the questions that follow.

c) Find the value 𝑥.

d) Find the size of ∠𝐴.

71° 60°

(2𝑥)°

(𝑥 + 15)° (3𝑥 − 15)° A B

1. Use a pair of compasses to draw circles with the following radii:

(a) 1.5 inches

(b) 2 inches

(c) 2.2 inches

2. Study the diagram below and answer the following questions.

(a) Name the plane figures you see in the diagram.

(b) Which pane figure has its vertices touching the edge of the other figure?

(c) Which plane figure is inside the other?

(d) PQ̅̅̅̅ is one of the sides of the figure on the inside, what part of the figure on the outside does PQ̅̅̅̅

represent?

Answer Keys Day 41:

1. (a)

2. (a) A triangle and a circle

(b) The triangle

(c) The triangle

(d) Chord

1. Using a pair of compasses, draw a circle of any convenient radius on the plain paper provided.

2. Label the center of the circle O.

3. Using a straightedge, draw a line segment to pass through the center O of the circle to construct the

diameter of the circle. Label it AB as shown below.

4. Using the compass, take the length of the radius; either OA̅̅ ̅̅ or OB̅̅ ̅̅ .

5. Without changing the width of the compass, endpoint B of the diameter AB as the center and make

two arcs that intersect the circle at two distinct points as shown below.

6. Label the points where the arcs intersect the circle as C and D as shown above.

7. Using a straightedge join point C to point D.

8. Similarly, join point A to point C and point A to point D respectively.

9. What is the name given to the plane figure formed inside the circle?

10. Using a protractor measure the size of ∠CAD, ∠ACD and ∠ADC. What do you notice about the

measures of these three angles?

11. Using a ruler, measure the lengths of AC̅̅̅̅ , AD̅̅ ̅̅ and CD̅̅̅̅ . What do you discover?

In this activity students will work in groups of four. They will draw an equilateral triangle inscribed in a

circle using a straightedge and a pair of compasses. They will need a ruler calibrated in inches to

measure the lengths of the line segments, a protractor to measure the angles and an A4 plain paper.

Answer Keys Day 41:

1. The circle should be large enough but it should fit on the paper provided.

2. No response

3. No response

4. No response

5. No response

6. No response

7. No response

8. No response

9. A triangle

10. ∠CAD = ∠ACD = ∠ADC = 60°; The angles are congruent

11. AC̅̅̅̅ = AD̅̅ ̅̅ = CD̅̅̅̅ ; The line segments are equal

Use a ruler and a compass to construct the largest possible equilateral triangles that can fit in each of

the given circles in questions 1-10. Use the radius indicated for your construction in each question.

1. Radius = 1 inch

2. Radius = 1.5 inches

For questions 11-20, use a pair of compasses and a straightedge only to construct an inscribed triangle

in a circle of the indicated radius. Use a ruler to accurately take the radii with your compass.

13. Radius = 1.8 inch

19. Radius = 2 inches

Answer keys

Day 41:

Use a pair of compasses and a straightedge only to construct an inscribed triangle in a circle of radius 2

inches.

Answer Keys Day 41:

1. At what angle does the sides of the square meet?

2. What is a perpendicular bisector

3. A circle has a radius of 3.5in, what would be its diameter.

4. Draw a circle of radius 1.5 in.

5. Draw the perpendicular bisector of the following line

Answer Key

Day 42

1. 90°

2. A line that divides another in to two equal parts and intersects it at a right angle

3. 7.0 𝑖𝑛

1. On the A4 plain paper, draw a circle of radius 2.5 inches and mark the center O.

2. Draw diameter to the circle and label it AB where A and B are its endpoints.

3. Construct the perpendicular bisector of the line and let it meet at arcs of the circles at C and D

respectively.

4. Connect the points of the arcs where the perpendicular lines passes through to form a polygon.

5. Measure the sides of the polygon.

6. Which kind of polygon is the one in 4 above? State your reason.

In this activity, we would construct a square inside a circle using a pairs of compass and a straightedge.

Students will work in groups of 3. Each group will require a plain paper, a pencil, a pair of compass and a

straight angle

Answer Keys

Day 42:

1 – 4.No response

5. Difference responses

6. Square. All sides are (approximately) equal

Draw inscribed squares in the following given circles.

Use the following statement to answer questions 11 – 18.

Consider a full diagram after inscribing a square in a circle

11. What is the name of the perpendicular bisector, of the diameter with respect to the square, that

spans between the vertices of the inscribed square drawn?

12. Explain your answer in 11 above.

13. What is the name of the perpendicular bisector of the diameter with respect to the circle that spans

between its vertices.

14. Explain your answer in 11 above.

15. Is the inscribed figure symmetrical?

16. Identify the lines along which it is symmetrical.

17. At what angle is the perpendicular bisector meeting the sides of the square?

18. The diameter and its perpendicular bisector divides the square into 4 equal parts, identify the name

of each part.

Use the following information to answer questions 19 – 20.

Draw the inscribed square in the following in the circles whose diameter are given.

19. 2.8 in

20. 4.2 in

Answer Keys Day 42:

11. Diameter

12. It passes through the center of the diameter which is the center of the circle and spans between the

arcs of the circle

13. Diagonal of a square

14. It extends from one vertex of a square to the opposite one

15. Yes

16. Symmetrical about the diameter, its perpendicular bisector and along the perpendicular bisector of

opposite sides. Thus, 4 lines of symmetry

17. 45°

18. Right Isosceles triangle

Draw an inscribed square of radius 2 in.

Answer Keys

Day 42

1. Study the figure below and answer the questions that follow.

(a) Using a straightedge and a pencil join the points of intersection of the arcs and the circle in the order:

ABCDEFA.

(b) How many sides does the plane figure formed in (a) above have?

(c) How many angles does it have?

(d) What type of polygon is formed when the points are joined as in (a) above.

(e) Measure the following angles using a protractor and write down your conclusion.

∠A, ∠B, ∠C, ∠D, ∠E and ∠F

(f) Measure the lengths of the following line segments in inches using a using a ruler and write down

your conclusion.

𝐴𝐵̅̅ ̅̅ , 𝐵𝐶̅̅ ̅̅ , 𝐶𝐷̅̅ ̅̅ , 𝐷𝐸̅̅ ̅̅ , 𝐸𝐹̅̅ ̅̅ and 𝐹𝐴̅̅ ̅̅

(g) Basing on the conclusions in (e) and (f), is this a regular polygon or an irregular polygon?

Answer Key Day 43:

(d) Hexagon

(e) All the angles are approximately congruent

(d) All the line segments have approximately equal lengths

(f) Regular polygon

1. Draw a circle of any convenient radius on the tracing paper using a compass and label the center O.

2. Carefully fold the paper along the center O of the circle in such a way that the two semi-circles formed

coincide.

3. Label the line segment formed by the crease of the fold along the center of the circle AB, illustrated

above.

4. What is the name given to AB̅̅ ̅̅ with reference to the circle?

5. Firmly fold the paper in such a way that endpoint B coincides with the center O of the circle. This fold

forms two vertices of the polygon.

6. Label the two vertices C and D respectively as shown below.

7. Similarly, firmly fold the paper in such a way that endpoint A coincides with the center O of the circle.

This fold forms two other vertices of the polygon.

8. Label the two vertices E and F respectively as shown above.

9. Using a straightedge and a pencil, join the points BCEAFDB in that order as shown below.

10. What is the name of the plane figure you have just constructed?

In this activity students will work in groups of three to construct a regular polygon inscribed in a circle

using paper folding. Each group will require an A4 size tracing paper, a straightedge, a compass and a

pencil.

Answer Keys Day 43:

1. No response

2. No response

3. No response

4. Diameter

5. No response

6. No response

7. No response

8. No response

9. No response

10. Hexagon

Use a ruler and a compass to construct the largest possible regular hexagon that can fit in each of the

given circles in questions 1-10. Use the radius indicated for your construction in each question.

1. Radius = 1 inch

For questions 11-20, use a pair of compasses and a straightedge only to construct an inscribed regular

hexagon in a circle of the indicated radius. Use a ruler to accurately take the radii with your compass.

13. Radius = 1.8 inch

19. Radius = 2 inches

Answer keys

Day 43:

Use a compass and a straightedge only to construct a regular hexagon inscribed in a circle of convenient

radius.

Answer Keys Day 43:

The circles will vary but the regular hexagon should be drawn accurately. All sides and angles of the

hexagon should be equal.

1. The diagram below shows a partly completed construction of an inscribed equilateral triangle.

Complete the construction.

2. Below is a diagram of a square and its diagonals. What is the angle of intersection of the diagonals?

3. Construct the perpendicular bisector to the line segments given below.

4. The diagram below shows a partly completed construction of a regular hexagon. Complete the

construction.

Answer Key Day 4

2. 90°

1. Position the needle of the compass at 0 mark of the ruler and extend it up to an in mark.

2. Without changing the width of the compass in step 1, draw a circle in the middle of the plane paper.

3. Draw horizontal diameter to the circles.

4. Construct a perpendicular bisector of the diameter of the circle as shown.

5. Join the intersections of the diameter with the intersection of the perpendicular bisector.

6. Which shape is formed by the lines joining the diameter and the perpendicular bisector.

In this activity, students will construct a square inscribed in a circle. Students are required to work in

groups at least three. Each group is required to have a pencil, a ruler, a plane paper and a compass.

Answer Keys

Day 44:

1-5. No response

6. Square.

In questions 1 to 3, construct an inscribed square in the circle with the given radius.

1. Radius = 1.2in

2. Radius = 1.5 in

3. Radius = 0.75 in

In questions 4 to 7, you are given circles with their diameters, construct an inscribed square in each

circle.

In questions 8 to 13, construct an inscribed triangle in the circle with the given radius.

8. 0.75 in

9. 1 in

10. 1.5 in

11. 2 in

12. 1 ∙ 4𝑖𝑛

13. 1 ∙ 2𝑖𝑛

From questions 14 to 19, you are given diameters of different circles. Draw the circle with the given

diameter and construct a regular hexagon inscribed in the circle.

14. 1.5 in

15. 2in

16. 3in

17. 4in

18. 2.8in

19. Construct a regular hexagon in the circle given below. O is the center of the circle.

20. A pesticide manufacturing company designed a cylindrical can for storing a pesticide. They decided

to make a regular hexagonal hole at its circular top such that the vertices of the hole are on the

circumference of the circular top. If the can had a radius of one inch, draw the top part alone and

construct the hexagonal hole.

Answer Key Day 44

1. The circle below has a radius of 1inch. Construct an inscribed hexagon in the circle.

Answer Keys

Geometry

Week 9

Weekly Assessments

Week #9 1. Construct an equilateral triangle inscribed in the

circle below.

2. Construct regular hexagon inscribed in the circle

below.

3. Construct squares inscribed in the circles below.

4. Construct perpendicular bisectors to the

following lines.

5. Line 𝐿1 passes through points 𝑋(−2, −6)

and 𝑌(−1,3). At point y, 𝐿2 intersects 𝐿1 at a

right angle.

a) Find the slope of 𝐿2.

b) Find the equation of 𝐿2.

6. Lines AB and CD are parallel. The equation of

AB is 5𝑦 = 7𝑥 − 36. Line CD passes through

point 𝐶(4,6).

a) Find the slope of CD.

b) Find the equation of CB.

Week 9 - KEYS

Weekly Assessments

Week #9 KEY 1. Construct an equilateral triangle inscribed in the circle below.

2. Construct regular hexagon inscribed in the circle below.

3. Construct squares inscribed in the circles below.

4. Construct perpendicular bisectors to the following lines. a)

5. Line 𝐿1 passes through points 𝑋(−2, −6) and 𝑌(−1,3). At point Y, 𝐿2 intersects 𝐿1 at a right angle.

c) Find the slope of 𝐿2.

d) Find the equation of 𝐿2.

9𝑦 = −𝑥 + 26

6. Lines AB and CD are parallel. The equation of AB is 5𝑦 = 7𝑥 − 36. Line CD passes through point 𝐶(4,6).

c) Find the slope of CD.

d) Find the equation of CB.

5𝑦 = 7𝑥 + 2

Unit 3 Test Name ____________________________________

Questions:

1. In the figure below lines PQ and RS are parallel. State whether the following angles are

corresponding, alternate interior or alternate exterior angles.

a) ∠4 and ∠5

b) ∠1and ∠5

2. What is the value of z?

Unit 3 Test Name ____________________________________

3. What is the sum of angles x, y and z?

4. Define triangle!

5. Find the measure of angle y.

Unit 3 Test Name ____________________________________

6. In the figure below isosceles triangle JKL is formed between the parallel lines AB and CD. Find the

value of angle ∠𝐽𝐿𝐾in terms of 𝛽.

7. ABC is an isosceles triangle. Line AB = 12 cm and line AC = 16 cm. Find the length of BD.

Unit 3 Test Name ____________________________________

8. In ∆𝑆𝑇𝑅, 𝑆𝑇 = 20 cm, 𝑇𝑅 = 16 cm 𝑎𝑛𝑑 𝑅𝑆 = 18 cm. The line segments AT, CR and BS are the

medians of ∆𝑆𝑇𝑅. What is the length of SC?

9. Draw the medians of the following triangle identifying any resultant features created as a result

of drawing the medians.

10. One of the base angles of an Isosceles triangle is 50°, find the size of all other angles.

Unit 3 Test Name ____________________________________

11. Bisect the line segment. Use a straightedge and a pair of compasses only.

12. Define line segment!

13. State whether the following statements are true or false.

a) A bisector of a line is also perpendicular to the line.

b) A bisector of a line passes through its midpoint.

14. List 3 main methods that are used to construct parallel lines.

Unit 3 Test Name ____________________________________

15. Use a compass and a straightedge to complete the construction of an angle bisector to ∠𝐴𝑂𝐶

below.

16. What is the name given to the plane figure formed inside the circle?

17. Define an inscribed triangle.

18. A circle has a radius of 4 cm, what would be its diameter?

19. Draw inscribed square in the circle.

Unit 3 Test Name ____________________________________

20. Here we have a square and its diagonals. What is the angle of intersection of the following

diagonals?

Unit 3 Test Name ____________________________________

Answers:

a) Alternate interior angles

b) Corresponding angles

2. 𝑧 = 59°

3. 180°

4. Triangle is a plane figure bounded by three line segments to form its edges and three vertices

formed between two adjacent edges.

5. 𝑦 = 79°

6. ∠𝐽𝐿𝐾 = 𝛽

7. 𝐵𝐷 = 6𝑐𝑚

8. 𝑆𝐶 = 10𝑐𝑚

10. 50° and 80°

Unit 3 Test Name ____________________________________

12. Line segment is a portion of a line between two endpoints.

a) True

b) True

1) The use of a set square

2) The use of angle transfer method

3) The use of parallelogram method

16. A triangle.

17. Inscribed triangle is a triangle drawn inside another plane figure such that the vertices of the

triangle touch the edge of the plane figure.

Unit 3 Test Name ____________________________________

18. 8cm

20. 90°

Geometry Complete Unit 3 - highschoolmathteachers.com · Unit 3 Pacing Chart...

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