Download - EXAMPLE 3
EXAMPLE 3 Use the SAS Similarity Theorem
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?
Lean-to Shelter
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.
Find the ratios of the lengths of the corresponding sides.
Shortest sides Longer sides
SOLUTION
RTNQ
43
2821 ==
SRPN
43==
2418
GUIDED PRACTICE for Examples 3 and 4
Explain how to show that the indicated triangles are similar.
The corresponding side lengths are proportional. The included angles R and N are right angles. So, SRI ~ PNQ by the SAS Similarity Theorem.
ANSWER
GUIDED PRACTICE for Examples 3 and 4
4. XZW ~ YZX
Explain how to show that the indicated triangles are similar.
Find the ratios of the lengths of the corresponding sides.
SOLUTION
XZYZ
129=
WZXZ
43=
43==
1612
GUIDED PRACTICE for Examples 3 and 4
Explain how to show that the indicated triangles are similar.
WXXY
43=
2015=
WXY XZY = 90°
The corresponding side lengths are proportional. The angles WZX and XZY are right angles.
ANSWER
So, XZW ~ YZX by the SAS and SSS Similarity Theorem.