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Geometry: Unit 8 – Proportions and Similar Polygons

2 5

12 2

x

x

8 2

2 3 4y y

3 2

4 6

x

Practice – Proportions and Similar Polygons pp 454-459 Name ________________________ Date ______________ Period ______ Solve each of the following proportions for the missing variable.

1. 2. 3.

Write a proportion for the given situation and solve for the missing variable. 4. During the 2003 NFL season, the Dallas Cowboys won 10 of their 16 regular-season games.

What is their ratio of wins to losses in simplest form?

5. The ratio of the side lengths of an isosceles triangle is 4:4:7 and its perimeter is 90cm. What is the length of the base of the triangle?

6. Given that5 25y x , find the ratio of x to y in simplest form.

Determine if the answer is always, sometimes or never true. A. _____________________

B. _____________________

C. _____________________

7. Two squares are similar.

8. If two polygons are congruent then they are also similar.

9. If two polygons are similar, then they are also congruent.

Geometry: Unit 8 – Proportions and Similar Polygons

0 1 2 3 4 5 60

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2

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4

5

6

x

y

D

E

F

0 1 2 3 4 5 60

1

2

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y

A

C

Use the properties of similar triangles to answer the following questions. 10. The ratio of the perimeter of rectangle ABCD to the perimeter of rectangle EFGH is 4:7. Find x. 11. Given WXYZ LPNM , determine the missing information.

A. _________m Y

B. __________X

C. ____________b .

D. If 12WZ , then a = _______

12. ABC DEF . The scale factor of ABC to DEF is 3

7.

A. If AB = 15, then DE = __________.

B. If EF = 42, then BC = __________.

13. Find the coordinates of B so that ABC DEF .

14. Determine if DOG CAT given that 4,DG 10,GO 8DO 12,AT 6CT and 15.AC

Why or why not? ___________________________________________________________ __________________________________________________________________________

x H G

F E

D C

B A

5

W

Z

X

Y

65

3 c

b N

M

L

P 2

a

10

7

32

Student Practice—Proving Triangles Similar

Name:_________________________

Statements Reasons

Given

If two sides of a triangle are congruent then the angles opposite are congruent.

Given

∆GHJ~ ∆MLK

Using Proportional Relationships SP

1. How could you use indirect measurement to find the height of the flagpole at your school?

2. Your friend determined that at point S, the

measure of the angle from the ground to the

top of a tree at point T is the same as the

measure of the angle from the ground to the

top of a rock formation at point R. Write an

expression, in terms of y, for the height of the

rock formation, in meters.

3. Irene places a mirror on the ground 24 ft from

the base of an oak tree. She walks backward until

she can see the top of the tree in the middle of

the mirror. At that point, Irene’s eyes are 5.5 ft

above the ground, and her feet are 4 ft from the

mirror. How tall is the oak tree? Explain.

Geometry- Similarity in Right Triangles SP

For #1-4 Find the geometric mean:

1. a=3 b=12 2. a=4 b=6

3. a=5 b=15 4. a=15 b=6

For #5-6 Find x:

5. 12 is the geometric mean of 6 and x.

6. 9 is the geometric mean of 3 and x.

Geometry- Similarity in Right Triangles SP

For #7-10 Find x: Leave answer in simplest radical form.

7. 8.

9. 10.

Geometry: Proportions in Triangles SP

A C E

B

D

Practice – Proportions in Triangles pp 481-487 Name _________________________ Date _____________________ Period _________

Write a proportion, then solve for the variable.

1. 2.

Use the triangles to the right.

3. Assume that BAC DCE . What additional information

would you need to prove that ABC CDE by AA~?

4. Assume that AB CD

BC DE . What additional information

would you need to prove that ABC CDE by SAS~?

5. Find the value of y. 6. Find the value of x.

7. In a new subdivision, three trapezoidal lots are

125 ft across the front. The lot lines on the side

are all perpendicular to the front. Find the length

of the property line across the back of each lot.

Write a proportion, then solve for the variable. 8. 9.

Write a proportion, then solve for the variable.

8

2

16

x

2 x

5 3

Lot A

Lot B Lot C

125 ft 125 ft 125 ft

420 ft

k

9 15

5

n

10.5

21

p

7

12

24

) )

12

x

6

7

8

x 9

15

12 9

y

Geometry: Proportions in Triangles SP

10. 11.

12. 13.

14. Is line p parallel to line q ? (YES OR NO)

A. ______ B. ______ C. ______

Write a proportion, then solve for the variable x.

15. 16.

Write a proportion and solve. Given ADH , DF bisects ADH and p q r .

17. AC = 8, CD = 3, AH = 15. Find AG and GH.

18. AF = 6, FH = 8, AC = 7, DH = 13. Find CD.

19. AD = 12, DH = 15, FH = 8. Find AF.

A

B

C

D

E

F G

H

p

q

r

2 x

9 x

10

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p

q

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q

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p

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x 12

4

Geometry – Unit 9 REVIEW

Unit 9 Review – Similar Polygons

1.Solve for x. 12 9

15 45

x

2. Find the geometric mean between 12 and 18.

3. The geometric mean of 4 and a number is 64. Find the number.

Tell me why the triangles are similar. Use AA~, SAS~, and SSS~

4. 5. 6.

(A) They are similar by AA~

(B) They are similar by SAS~

(C) They are similar by SSS~

(D) They are not similar.

(A) They are similar by AA~

(B) They are similar by SAS~

(C) They are similar by SSS~

(D) They are not similar.

(A) They are similar by AA~

(B) They are similar by SAS~

(C) They are similar by SSS~

(D) They are not similar.

7. A parallelogram has the dimensions shown below. Which set of dimensions would produce a

similar figure?

A. 44 cm, 88 cm

B. 60 cm, 150 cm

C. 2.5 cm, 5 cm

D. 10 cm, 22 cm

A

S

T W B

12 cm

30 cm

Geometry – Unit 9 REVIEW

8. Use the similar polygons.

x = ______

UVWX is _____times the size of ABCD.

9. We know ∆ABC~∆EDC. Find…

_____A

_____B

m = ______

10. If BD = 12, AC = 24, DE = 14, find CE.

11.

12. To find the length of a pond, Ana took some measurements. She recorded them on this diagram.

What is the length of the pond?

x

A

C

B E

D

12

8 10

4

m

E

A B

C D

CE = _______

B

A 21

3

5 m

) )

m = ______

Geometry – Unit 9 REVIEW

13. Find x.

14. Find XY.

15. Use the picture.

X = _______

Y = _______

17. On a sunny day, Alex’s shadow is 2.9 m long,

while the shadow of a tower is 11.3 m long.

If Alex is 1.8 m tall, calculate the height of the tower.

Geometry – Unit 9 REVIEW

18. Two ladders are leaned against a wall.

The 10 foot ladder reaches 8 feet up the wall.

How much further up the wall does the 18-foot ladder reach?

19. A map of New York is shown to the right.

Find the distance between

2nd and 3rd street.

20. Estimate the height of the rock wall.