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7-3 Additional PracticeProving Triangles Similar

For Exercises 1–4, if the two triangles are similar, state why they are similar. If not, state that they are not similar.

1.

J L

M O

N

K

2.

N L

MO P

Q

30

15

13 1326 26

3. A

D

BE

C

4.

28

1014

5

T V

U

W

X

For Exercises 5 and 6, use the triangles shown.

5. What is FE?

6. What is DE?

For Exercises 7 and 8, what is the value of x?

7.

10 6

12

D

A C x

B

F

E 8.

3 21

14x

9. Are triangles ABC, DEF, and 10. The width of the pond shown HIJ similar? Explain. is x ft. What is the value of x?

4 9

1215

8

610

3 5

A H I

JF D

E

C

B

48 ft

60 ft

80 ft

A B

D

E

Cx ft

89° 89°35°

35°36

20 2440

RF

D

E

Q

P

not similar

not similar

43.2

x = 20

yes; by SSS ~x = 100 ft

48

SSS ~

SAS ~

x = 2

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7-4 Additional PracticeSimilarity in Right Triangles

1. Name the right triangles that are similar to △QRS.

S

Q

R

T

For Exercises 2–5, find the values of x and y.

2. 3.

4. 5.

6. Devin says that since the diagonals of the kite intersect at right angles, the small right triangles are similar to both the left half and the right half of the kite. Is he correct? Explain.

7. Isabel and Helena have built a frame and covered it with cloth. The frame is in the shape of a right triangle, △ABC, with side lengths 6 ft, 8 ft, and 10 ft. They use a vertical pole ̄ AE to raise corner A 3 ft, as shown. What is the distance ED from the base of the pole to the edge of the frame? Round to the nearest foot.

9

1

x

y

14

6

x y

12

4

x

3612 y

△QST, △SRT

x = 2 √ ___

30 ; y = 2 √ ___

21

x = 32 __ 3

Answers may vary. Sample: He is correct only if the vertical diagonal divides the kite into two congruent right triangles; otherwise he is incorrect.

4 ft

x = √ ___

10 ; y = 3 √ ___

10

y = 8 √ ___

2

C

D

B

A

E 10 ft

3 ft

8 ft

6 ft

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7-5 Reteach to Build UnderstandingProportions in Triangles

1. Match each diagram to the appropriate conclusion.

A C

NM

B

A C

NM

B

A CM

B

Then...

AM ___ MB = CN ___ NB

Then...

AM ___ CM

= AB ___ CB

Then...

‾ MN ∥ ‾ AC

MN = 1 __ 2 (AC)

2. Marta incorrectly states that PS = SR. Fill in the blanks to explain Marta’s error and find the correct value of SR.

Marta assumes incorrectly that because ̄ QS is the of ∠PQR, S must be the midpoint of ̄ PR .

However, to find the correct value of SR, she should apply the Triangle- Angle-Bisector Theorem.

PS __ SR

= PQ ___

RQ

10 __ SR

= 12 __ 36

10 · = · SR

= SR

3. Fill in the blanks to find XJ.

XJ __ JY = ZK ___ KY

XJ __ 20

= 9 __ 12

· XJ =

XJ =

If... If... If...

Q

P RS

3612

10

Y

Z

KJ

X

12

9

20

angle bisector

36 30

180 15

12

12

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7-5 Additional PracticeProportions in Triangles

Find the missing lengths. Round to the nearest tenth as needed. 1. x 2. y 3. z

Solve for x.

4. 2

6

9x

5. x + 1x

1512

6.

72x

8 16

7.

x 6

5 3

8.

x + 4x

x – 2 9

9.

7.52.5x

3x 4

10.

x + 4

x + 2x

3 11.

x

16 12

9

12. 6

9

x – 4

x

13. River claims that he can write two different proportions to find x. What are the two proportions?

14. The flag of Antigua and Barbuda is similar to the image shown, where DE || CF || BG.

a. Nora sketched the flag for a mural. The labels show the length of the lines in feet. What is the value of x?

b. What type of triangle is △ACF? Explain.

162.17.2

3

10

4

4

8

12

7

2

12

12 __ 16

= 9 __ x ; 12 __ 9 = 16 __ x

isosceles; because CA = FA

4

x

16 12

9

4x + 5

4x – 43x

21

D

C

B G

F

E

A

yz

x

7

3

5.6

8.75 7

25

4

5

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