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