CK-12 Geometry-Concepts

http://www.ck12.org Chapter 7. Similarity

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CK-12 Foundation: Chapter7SSSSimilarityB

Vocabulary

Two triangles aresimilarif all their corresponding angles arecongruent(exactly the same) and their corresponding
sides areproportional(in the same ratio).

Guided Practice

Determine if any of the triangles below are similar. Compare two triangles at a time.

1. Is 4 ABC∼4DEF?


2. Is 4 DEF∼4GHI?


3. Is 4 ABC∼4GHI?

Answers:

1. 4 ABCand 4 DEF: Is^2015 =^2216 =^2418?

Reduce each fraction to see if they are equal.^2015 =^43 ,^2216 =^118 , and^2418 =^43.
4
36 =

11

8 ,^4 ABCand^4 DEFarenotsimilar.

2. 4 DEFand 4 GHI: Is^1530 =^1633 =^1836?

15

30 =

1

2 ,

16

33 =

16

33 , and

18

36 =

1

2.

1

26 =

16

33 ,^4 DEFisnotsimilar to^4 GHI.

3. 4 ABCand 4 GHI: Is^2030 =^2233 =^2436?
   20
   30 =

2

3 ,

22

33 =

2

3 , and

24

36 =

2

3. All three ratios reduce to

2

3 ,^4 ABC∼4GIH.

Explore More

Fill in the blanks.

1. If all three sides in one triangle are __ to the three sides in another, then the two triangles
   are similar.


2. Two triangles are similar if the corresponding sides are _____.

Use the following diagram for questions 3-5.The diagram is to scale.