1. 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

2. 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 sidesLonger sides AB FG 3 2 9 6 == AC FH 3 2 15 10 == The lengths of the sides that include A and F are proportional.

3. 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.

4. 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 sidesLonger sides SOLUTION CA CD 3 5 18 30 == BC EC 3 5 9 15 == 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.

5. 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 sidesLonger sides SOLUTION RT NQ 4 3 28 21 == SR PN 4 3 == 24 18

6. 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

7. 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 XZ YZ 12 9 = WZ XZ 4 3 = 4 3 = = 16 12

8. GUIDED PRACTICE for Examples 3 and 4 Explain how to show that the indicated triangles are similar. WX XY 4 3 = 20 15 = WXYXZY = 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.