©oiD:::J()of!!..$:()oOJ::EI

I

NAME DATE _;---- PERIOD __

Skills Practice

Similar PolygonsDetermine whether each pair of polygons is similar. Justify your answer.

1. 3 6 2. 2 5 3. 2 5

'0:0· 2g]2D 101D2 3 32 5 55

6Yes; corresponding Yes; corresponding 1 2angles are congruent angles are congruent No' -""-., 3 5

and l = 4 2 28

and - =-.6 5 5

4. 3 4 5. ..:tJ: 6. 10{J3Q 1:L14 6 '00:0:, 1014 6 10

26No; corresponding Yes; corresponding Yes; correspondingangles are not angles are congruent angles are congruentcongruent. 14 14 14

and 160is the ratio forand 26 = - = -26 26

the lengths of all sixsides.

If each pair of polygons is similar, find the values of x and y.

20 D30

20~20 x

20 y

164~

8. 9.7. 20Azjx~'6

6 12

x = 30,y = 30 x = 6,y = 24x = 8,y = 10

11o 12.10. 11. 6

10~4d16Y

9x

x = 8,y = 20 x=11,y=11 x = 15,y = 24

357© Glencoe/McGraw-Hili Geometry: Concepts and Applications

NAME DATE PERIOD __

Practice

Similar Polygons

Determine whether each pair of polygons is similar.Justify your answer.

1.'0nOO15 ft

8ft

2. 3cm-:>6C~

70m12ft

Yes; the angles are congruentand 10 - 8

15-12'

3. :~~~~~~~~JiT4-ft--O

8ft

Yes; the angles are congruent

and t = /5'4. A

13 in.

B

13 in.

ELL---,--,2...,.in-.--O-!,J-----,-,2"'i,-n.----=. C

Yes; the angles are congruentand 26 =.rr

24 12'

In the figure below, trapezoid ABeD - trapezoid EFGH.Use this information to answer Exercises 5-9.

12ft

no; ~ "" 182

"r,-------'-1~' :\H Y G

5. ListalJpairs of corresponding angles. LA & LE; LB& LF; LC& LG; LD& LH

6. Write four ratios relating the corresponding sides. AB. BC. CD. DAEF' FG' GH' HE

7. Write a proportion to find the missing measure x.Then find the value ofx. Sample answer: f = 182;4

8. Write a proportion to find the missing measure y.Then find the value ofy. Sample answer' L = rr. 16.1

. 11' 8' 2

9. Write a proportion to find the missing measure z.Then find the value of z. Sample answer: f = 182;7!

358© Glencoe/Mc'Sraw-Hlll Geometry: Concepts and Applications

rCDeneno:::lillI

!:S

NAME DATE PERIOD __

Study Guide

Similar TrianglesThere are three ways to determine whether two triangles are similar.

Show that two angles of one triangle are congruent to twoangles of the other triangle. (AA Similarity)

Show that the measures of the corresponding sides of thetriangles are proportional. (SSS Similarity)

Show that the measure of two sides of a triangle areproportional to the measures of the corresponding sides of theother triangle and that the included angles are congruent.(SAS Similarity)

=

Example: Determine whether the triangles are similar.Explain your answer. ~J

Since li? = ~ = lQ the triangles are 15 2012 20 16'

similar by SSS Similarity. H 25 K

Q

1~

P 20 R

Determine whether each pair of triangles is similar. Give areason for your answer.

l'B~ G<£JL~c FA

yes; AA3. M

,,~ ,41'z y

2, N

,~L 8 M

4.~e~

o E

U

9~

T 6 S

no; no information on angles yes; AAIdentify the similar triangles in each figure. Explain why theyare similar and find the missing measures.

5. If MN II AB, find AB, BC,and EN.

c2:::\4~ 8 '\

A 8

·6. IfMNPQ is a parallelogram,=:»2~

M 50 N

LQSM- LPSR- LNMR; AA;332- 132- 20

3' 3'© Glencoe/McGraw-Hili 361 Geometry: Concepts and Applications

NAME DATE PERIOD __

Skills Practice

Similar TrianglesDetermine whether each pair of triangles is similar. If so, tell which similarity test isused and complete the statement.

L 2, 3,A Z 8 6 A A R

~~ ,~~ ~8 DZ6y6 12

C 8 M Y o 3 N Y8 c

6.ABC - 6. I 6.MNO - 6. I 6.BAC - 6. Iyes; ZYM; SAS yes; YBA; SSS yes;ZYR; AA

4. 5. 6. »A A F R :l

NY ,1·2>, ,~ ~~:e

0 (l)F E G0 """l

6.DEF - 6. I 6.DYA - 6. I 6.FGI - 6. I ~not similar yes;RMZ; AA not similar r

(!)CIJCIJ0

Find the value of each variable. ::::JCO

7. 8. 9, I

~ r: 6:L1 ~~24 36 ~x

24 12

Y24

x=8 X = 16,y = 24 x = 3,y = 7

10. 11. 12.30 20

'~ ~x~ 24 ~

~~20 15 30 20 42

X = 6,y = 18 x = 16,y = 24 x=20,y=28

© Glencoe/McGraw-Hili 362 Geometry: Concepts and Applications