EXAMPLE 3 Use the SAS Similarity Theorem

Lean-to Shelter

You are building a lean-to shelter starting from a tree branch, as shown. Can you construct the right end so it is similar to the left end using the angle measure and lengths shown?

EXAMPLE 3 Use the SAS Similarity Theorem

Both m A and m F equal = 53°, so A F. Next, compare the ratios of the lengths of the sides that include A and F.

~

SOLUTION

Shorter sides Longer sides

ABFG

32

96 ==

ACFH

32

1510 ==

The lengths of the sides that include A and F are proportional.

EXAMPLE 3 Use the SAS Similarity Theorem

ANSWER

So, by the SAS Similarity Theorem, ABC ~ FGH. Yes, you can make the right end similar to the left end of the shelter.

EXAMPLE 4 Choose a method

Tell what method you would use to show that the triangles are similar.

Find the ratios of the lengths of the corresponding sides.

Shorter sides Longer sides

SOLUTION

CACD

35

1830 ==

BCEC

35

915 ==

The corresponding side lengths are proportional. The included angles ACB and DCE are congruent because they are vertical angles. So, ACB ~ DCE by the SAS Similarity Theorem.

GUIDED PRACTICE for Examples 3 and 4

3. SRT ~ PNQ

Explain how to show that the indicated triangles are similar.

ANSWER

R N and = = , therefore the

triangles are similar by the SAS Similarity Theorem.

SRPN

RTNQ

4 3

GUIDED PRACTICE for Examples 3 and 4

4. XZW ~ YZX

Explain how to show that the indicated triangles are similar.

XZYZ

WZXZ

43= WX

XY= = WZX XZY and

therefore the triangles are similar by either SSSor SAS Similarity Theorems.

ANSWER