CK-12 Geometry Concepts

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

AB

EF=

10

20 =

1
2
Since the ratios are not all the same, the triangles are not similar.

Watch this video for help with the Examples above.

MEDIA

Click image to the left for more content.

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.

Practice

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.

3. Are the two triangles similar? Explain your answer.


4. Are the two triangles congruent? Explain your answer.