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Geometry
Unit 4
Summer
Monday July 19, 2021 Activator How could you get away from the Pink Ghost?
(3 Left, 6 up)
A slide (move) will be called a Translate.
𝑇( −3 , 6 )Page #3
Lesson 4.1
Today’s Objective
Students will be able to translate (slide) shapes.
Lesson 4.1
What is a translation in Geometry? It is a slide.
Today’s New Vocab (1 of 4)
What is the name of thePre-Image(Original) Shape?
What is the name of theImage (New) Shape?
∆𝐴𝐵𝐶
∆𝐴′𝐵′𝐶′The Prime (Apostrophe’) means moved.
Today’s New Vocab (2 of 4)Translate rectangle ABCD.What is the translation? 𝑇(9,4)
Y
x
A is taken to A’
B maps to B’
C’ is the image of C <BCD maps to <B’C’D’
DA is taken to D’A’
Today’s New Vocab (3 of 4)Translate ∆𝐴𝐵𝐶 𝑠𝑜 𝑡ℎ𝑎𝑡 𝐴′𝑖𝑠 𝑎𝑡 2,4
Write thetranslation?
𝑇(6,0)
Describe the Translation.
Slide 6 right, then Slide 0 up
Draw New Triangle ∆𝐴′𝐵′𝐶′
Today’s New Vocab (4 of 4)Translate ∆𝐴𝐵𝐶 𝑠𝑜 𝑡ℎ𝑎𝑡 𝐵′𝑖𝑠 𝑎𝑡 −4,−1
Write thetranslation?
𝑇(−3,−2)
Describe the Translation.
Slide 3 left, Then Slide 2 down
Draw New Triangle ∆𝐴′𝐵′𝐶′
B’Page #4
Lesson 4.1
GWQ’s Skip #11
#1#2#3#4#5
#6#7#8#9#10
Page #1Lesson 4.1
1,2,6,10,83,4,5,13,91,2,6,10,8
1,2,6,10,8
1,2,6,10,8
1,2,6,10,83,4,5,13,9
3,4,5,13,9
3,4,5,13,9
3,4,5,13,9
Monday July 19, 2021 Work Period
.
Describe the translation.Slide 3 right and 4 down What is the Image of given point A? What is A’?
+3 -4(-5+3, 2-4)
(-2, -2)
(-2, -2)(-2, -2) Page #4
Lesson 4.1
Monday July 19, 2021 Exit Ticket
.
Determine the translation. What is B and D’ ?
𝑇(1,−3)
D’ is (-5, -4)
B is (-6, 4)
Tuesday July 20, 2021 Activator Do these two rotations result in the same image? YES Can you name another two rotations? YES, 180 and 180
Progress report grades are on
the wall.
Green Purple Pre-Image Image
Today’s Objective
Students will be able to rotate shape 90, 180, and/or 270 degrees.
Lesson 4.3
Today’s New Vocab (1 of 4)Rotate any point 90 and 180 degrees clockwise
the point (1, 5)90 clockwise (5, -1)
180 clockwise (-1, -5)
Rule (y, -x) Switch (5, 1)
(-1, 5)Switch
Change the new y or old x
Change
Change
Today’s New Vocab (2 of 4)Rotate the figure 90 degrees clockwise
Clockwise rule (y, -x)
E ( -4, 8)H (-2, 5)G (-4, 3)F ( -7, 5)
E’ ( 8, 4)H’ (5, 2)G’ (3, 4)F’ ( 5, 7)
E’
H’G’
F’
Today’s New Vocab (3 of 4)Rotate 90 degrees counter-clockwise
K (-2, 5) (5, 2)(2, -5)
K’(-5, -2)
L (1, 1) (1,-1)(-1,-1)
L’ (-1, 1)
Convert the turn to clockwise
M (-3, 1) (1, 3) (3, -1)
M’ (-1, -3)
Switch then change
L’
M’K’
Today’s New Vocab (4 of 4)A translation of𝑇(0,0) maps “ onto ”
The same reflectiontwice lands “ onto ”
Two rotations of 180 lies “ onto ”
Group Work Questions
#1#2#3#4#5
#6#7#8#9#10
2, 5, 11
2, 5, 11
3, 6, 7, 11
3, 6, 7, 11
2, 5, 11
2, 5, 11
3, 6, 7, 11
3, 6, 7, 11
2, 5, 113, 6, 7, 11
Page #5Lesson 4.2
Tuesday July 20, 2021 Work Period
.
R (-2, 3)S (4, 4)T (2, -2)
R’ (3, 2)S’ (4,-4)T’ (-2,-2)
(3,-2)(4, 4)(-2,2)
Pre-Image ImageSwitch
Change
RS
T
R’
S’T’
Tuesday July 20, 2021 Exit Ticket
.
𝑅270 𝑖𝑠 𝑎 Rotation 270 degrees counter-clockwise
𝑅270 = 𝑅−90
Counter-clockwise and clockwise
Positive Numbers Negative
B
C
B’ (1,-5)
C’ (-2,3)C’
B’
Wednesday July 21, 2021 Activator If one base angle is 70, what isthe measure of the vertex angle?
70 + 70 + x = 180
140 + x = 180
-140 -140x = 40
Today’s Objective
Students will be able to solve problems with isosceles triangles
and triangle sum.
Lesson 4.4
Today’s New Vocab (1 of 4)
65
2525
65
AD is the Line of ReflectionAD is Perpendicular ( ) to BC
What is m<DAC? 25 What is m<CDA? 90What is m<BAD? 25What is m<BDA? 90
Today’s New Vocab (2 of 4)What is the measure of <E ?
E
20 + 20 + <E = 180
40 + <E = 180-40 -40
<E = 140
Today’s New Vocab (3 of 4)Given: Trapezoid ABCD contains 4 isosceles triangles.
What is the measure of <CED ?
E
25 + 25 + x = 18050 + x = 180-50 -50
x = 130
Today’s New Vocab (4 of 4)
What is the measure of <C? 30 + 90 + <C = 180
120 + <C = 180-120 -120
<C = 60
AD is a perpendicular angle bisector and <BAC is 60.
GWQ’s 1A: Find <BAC
#1#2#3#4#5
#6#7#8#9#10
1ABC, 5 , 8
1ABC, 5 , 8
2ABC, 6 , 8
2ABC, 6 , 8
1ABC, 5 , 8
1ABC, 5 , 8
2ABC, 6 , 8
2ABC, 6 , 8
1ABC, 5 , 8 2ABC, 6 , 8
Page #13Lesson 4.4
Wednesday July 21, 2021 Work Period
.
Determine the value of angle <BCD in the picture.
<A + <ACB + <B = 180x + x + 80 = 180
2x + 80 = 180
2x = 100
x = 50
50 + <BCD = 180
<BCD = 130÷ 2 ÷ 2
− 80 − 80
− 50 − 50
Wednesday July 21, 2021 Exit Ticket
.
My house roof is in the shape of an isosceles
triangle. The vertex angle formed at the peak of the
roof is 104°. What is the measure of the base angles?
104 + x + x = 180104 + 2x = 180
2x = 76
x = 38
-104 -104
÷ 2 ÷ 2
Thursday July 22, 2021 Activator What is point A (2, 6)
reflected over the x-axis?
What is point A (2, 6)reflected over the y-axis?
A’( 2, -6)x doesn’t change.
A’’( -2, 6)y doesn’t change.
A’’
A’
Today’s Objective
Students will be able to reflect shapes over the x and y axes.
Lesson 4.5
Today’s New Vocab (1 of 3)Translate AB 𝑇(0,2)
A’( -3 , 0 ) B’( 1 , 0 )
Translate CD 𝑇(1,0)C’( 4, 1 ) D’( 4 , -4 )
A’ B’
Today’s New Vocab (2 of 3)Rotate AB 90 clockwise
A’( 2 , 3) B’( 2 , -1)
A (-3, 2) B (1,2)
Switch (2, -3) Switch (2, 1)
Switch then change
A’
B’
Today’s New Vocab (3 of 3)Reflect AB over x-axis
Reflect CD over y-axis
A’( -3 , -2 ) B’( 1 , -2 )
C’( -3 , 1 ) D’( -3 , -4 )
C’
D’
Group Work Questions
#1#2#3#4#5
#6#7#8#9#10
1, 6, 7abcd
5, 4, 7abcd
2, 3, 8abcd
1, 6, 8abcd
2, 3, 7abcd
1, 6, 8abcd
5, 4, 7abcd
2, 3, 7abcd
5, 4, 8abcd 1, 6, 7abcd
Page #17Lesson 4.5
Thursday July 22, 2021 Work Period
.
A’ ( 1 , 1 )
B’ ( 3, -1 )
C’ ( 1 , -4 )
𝑅(−90)
Rotation? Yes
Thursday July 22, 2021 Exit Ticket
.
A’ ( -2 , -1 )
B’ ( 0 , 1 )
C’ ( 3 , -1 )
𝑇(−1,−2)
Translation? Yes
Test 4 Info
#__ is worth double points.No work needed on #____All other questions must have work.
Friday July 23, 2021
Test 4 InfoMonday July 26, 2021