Name_____________________________________________Date____________________Period__________

Worksheet: Section 7.1

Examples #1-4: Graph the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor. 1. 2.

3. 4.

y

x

y

x

2,4 ,

34,4 , 3,2 ;

2

with vertices

and

JKP J

K P k

-2,4 , -2,-2 ,

-4,-2 -4,2 ; 0.5

Trapezoid with

vertices

and

ABCD

A B

C D k

4,4 ,

30,0 , 8,0 ;

4

with vertices

and

DGF D

G F k

-2,0 ,

0,2 , 2,-2 ; 3

with vertices

and

DGF D

G F k

y

x

y

x

Examples #5-6: Graph the image of each polygon with the given vertices after a dilation centered at the indicated center with the given scale factor.

5. 6.

y

x

y

x

2,2 , 2,0 , 0,1

1,2 ; 4,-2 3

Quadrilateral with

vertices

and

WXYZ

W X Y

Z k

-2,0 , 0,2 ,

2,0 0,-2 ; -4,-4 2.5

Quadrilateral with

vertices

and

MPQR

M P

Q R k

Name_____________________________________________Date____________________Period___________

Worksheet: Section 7.3 – Part II

1.

2.

5, 2.5

6, 3

2 4

Given:

Prove:

AB DE

BC EF

ABC DEF

Given: is a

Prove:

NPRV

NWO SWT

3.

4.

Given: is an altitude

is an altitude

Prove:

SP

RT

NRT NSP

2, 6, 3.2,

9.6, 4.1

12.3

Given:

Prove:

PIG COW

IP OC PG

CW IG

OW

Name_____________________________________________Date____________________Period__________ Worksheet: Section 7.3 – Part III

1.

2.

2, 8

3, 12

Given:

Prove:

AB BC

AE ED

BE CD

5, 2, 4

8, 15, 6

Given:

Prove:

WU WX UX

ZU YZ YX

W Y

3.

4.

Given: is a trapezoid

with bases &

Prove:

ABCD

AB DC

DP CP

PB PA

6, 4,

8, 3

Given:

Prove:

AC CD

BC CE

AB AC

ED EC

Name: __________________________

Unit 7 – Celebration of Knowledge Review – Day 1

For 1 – 2, solve each proportion.

1. 12 21

44 x 2.

40 3 1

27 2 1

x

x

1.___________

2. ___________ For 3 – 4, determine whether the two polygons are similar below. Justify your answer! 3.___________ 4.___________

8. Determine whether the triangles below are similar. If so, tell Which similarity is used and complete the statement (order counts). 8.____________________

15. If D, E, and F are the midpoints of their respective sides, complete the following statements.

For 18 – 20, draw and diagram using the given information and answer each question.

For 21 and 22, Find the value of the missing variable. 21. 22. 21._______________ 22._______________

For 26 – 30, use the diagram to the right. Determine the length of each segment.

26. AG 27. FC

28. ED 29. AE Given the following polygons 𝑨𝑩𝑪𝑫𝑬~𝑲𝑷𝑵𝑴𝑳. Find the following.

30. AE 31. ED 32. Perimeter Ratio 33. A right angle is divided into two angles whose measures are in the ratio of 2 to 7. Find the measure of the smaller angle. 34. The ratio of the measures of the angles of a triangle is 2:2:14. What is the measure of each angle?

Name______________________________ Date_____________ Period_____

Unit 7 – Celebration of Knowledge Review #2 1. The triangles shown are similar. Which of the following is not a correct statement?

A.

𝐴𝐵

𝑋𝑌=

𝐵𝐶

𝑌𝑍 C.

𝐶𝐴

𝑍𝑋=

𝐵𝐴

𝑌𝑋

B. 𝐵𝐶

𝑌𝑍=

𝐴𝐶

𝑋𝑌 D.

𝐴𝐶

𝑋𝑍=

𝐴𝐵

𝑋𝑌

2. On the coordinate grid below, one triangle is drawn and two vertices for a second triangle are also

shown. Which coordinates for the third vertex will form another triangle that is similar to the one

drawn?

A. (6, −1)

B. (6, −7)

C. (7, −1)

D. (10, −1)

3. Find the length of 𝑃𝑆̅̅̅̅ in the diagram below.

A. 𝑃𝑆 = 5

B. 𝑃𝑆 = 6

C. 𝑃𝑆 = 8

D. 𝑃𝑆 = 18

4. What is the value of x in the figure below?

A. 𝑥 = 4

B. 𝑥 = 5

C. 𝑥 = 6

D. 𝑥 = 7

5. What is the value for 𝑥 ?

A. 𝑥 = 18

B. 𝑥 = 16

C. 𝑥 = 12

D. 𝑥 = 3

6. In the figure below, what is the length of 𝐴𝐵̅̅ ̅̅ ?

A. 𝐴𝐵 = 7

B. 𝐴𝐵 = 11

C. 𝐴𝐵 = 16

D. 𝐴𝐵 = 20

7. Two triangles are similar and the ratio of each pair of corresponding sides is 2: 1 . Which

statement regarding the two triangles is not true?

A. Their perimeters have a ratio of 2: 1

B. The scale factor is a ratio of 2: 1

C. Their corresponding angles have a ratio of 2: 1

D. Their areas have a ratio of 4: 1

8. What is the value of 𝑛 ?

A. 𝑛 = 39

B. 𝑛 = 54

C. 𝑛 = 63

D. 𝑛 = 90

9. In ∆𝐿𝑀𝑁, 𝑆 is the midpoint of 𝐿𝑀̅̅ ̅̅ , 𝑇 is the midpoint of 𝑀𝑁̅̅ ̅̅ ̅, and R is the midpoint of 𝐿𝑁̅̅ ̅̅ . Given

the following, what is the perimeter of ∆𝑅𝑆𝑇 ?

𝐿𝑆 = 8.2𝑥

𝑆𝑇 = 4.3𝑥

𝑀𝑁 = 6𝑥

A. 11.4𝑥

B. 15.5𝑥

C. 18.4𝑥

D. 18.5𝑥

11. Apply the dilation 𝐷: (𝑥, 𝑦) → (4𝑥, 4𝑦) to the triangle given below. Which of the

following is the perimeter of the image?

A. 41.9 𝑢𝑛𝑖𝑡𝑠

B. 40.5 𝑢𝑛𝑖𝑡𝑠

C. 20.5 𝑢𝑛𝑖𝑡𝑠

D. 9.2 𝑢𝑛𝑖𝑡𝑠

12. What is the length of 𝐴𝐶̅̅ ̅̅ ?

A. 𝐴𝐶 = 28

B. 𝐴𝐶 = 26

C. 𝐴𝐶 = 24

D. 𝐴𝐶 = 15

13.

In the diagram below 𝐵𝐷̅̅ ̅̅ , 𝐷𝐹̅̅ ̅̅ , and 𝐵𝐹̅̅ ̅̅ are midsegments and 𝐵𝐶 = 10 and 𝐴𝐸 = 12. Compare the

perimeters of ∆𝐶𝐷𝐵 and ∆𝐷𝐸𝐹, then choose the statement below that is true.

A. The perimeter of ∆𝐶𝐷𝐵 is greater.

B. The perimeter of ∆𝐷𝐸𝐹 is greater.

C. A relationship cannot be determined.

D. The perimeters are the same.

14. Which method cannot be used in a coordinate proof to prove ∆𝐴𝐵𝐶~∆𝐴𝐷𝐸?

A. Use the Distance Formula to show 𝐴𝐵

𝐴𝐷=

𝐴𝐶

𝐴𝐸, and ∠𝐴 ≅ ∠𝐴 by the Reflexive Property of

Congruence. (𝑆𝐴𝑆~)

B. Use the Distance Formula to show 𝐴𝐵

𝐴𝐷=

𝐴𝐶

𝐴𝐸=

𝐵𝐶

𝐷𝐸 . (𝑆𝑆𝑆~)

C. Use the Reflexive Property of Congruence to show ∠𝐴 ≅ ∠𝐴, then measure to show

∠𝐴𝐵𝐶 ≅ ∠𝐷. (𝐴𝐴~)

D. Use the slope formula to show that the slope of 𝐵𝐶̅̅ ̅̅ and 𝐷𝐸̅̅ ̅̅ are equal so 𝐵𝐶̅̅ ̅̅ ∥ 𝐷𝐸̅̅ ̅̅ and

corresponding angles are congruent. (𝐴𝐴~)

16. The Hopewell people were Native Americans whose culture flourished in the central Ohio Valley

about 2000 years ago. The Hopewell people constructed earthworks using triangles, including

those below.

The diagram below shows the layout of some Hopewell earthworks. The centers of the Newark

Octagon, the Newark Square and the Great Circle were at the corners of the shaded triangle.

The three right triangles surrounding the shaded triangle form a rectangle measuring 12 units by

14 units. Which of the Hopewell triangles is similar to Triangle 1, Triangle 2, and Triangle 3 in

the diagram?

A. Triangle 1~Triangle 𝐴

Triangle 2~Triangle 𝐹

Triangle 3~Triangle 𝐶

C. Triangle 1~Triangle 𝐷

Triangle 2~Triangle 𝐹

Triangle 3~Triangle 𝐶

B. Triangle 1~Triangle 𝐴

Triangle 2~Triangle 𝐵

Triangle 3~Triangle 𝐶

D. Triangle 1~Triangle 𝐷

Triangle 2~Triangle 𝐵

Triangle 3~Triangle 𝐶

18.

Given: BE is a midsegment of ACD

AE BAProve: =

AD CA

A

E

C

B

D

19.

E

D

B C

A

F

20.

E

D

B

CA

21.

Given: ΔABC is isosceles with base BC

BD=4, BE=6, EC=9, FC=6

Prove: BDE CFE

Given: A EDC

BC is an altitude

AC ABProve: =

DC DE

Given: AB=8, AE=4, BE=6

CE=18, ED=12, CD=24

Prove: AB CD