EXAMPLE 3 Use the SAS Similarity Theorem Leanto

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

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. SOLUTION Find the ratios of the lengths of the corresponding sides. Shorter sides Longer sides BC 9 CA 18 3 3 EC = 15 = 5 CD = 30 = 5 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 Explain how to show that the indicated triangles are similar. 3. SRT ~ PNQ ANSWER N and SR = RT = 4 , therefore the PN NQ 3 triangles are similar by the SAS Similarity Theorem. R

GUIDED PRACTICE for Examples 3 and 4 Explain how to show that the indicated triangles are similar. 4. XZW ~ YZX ANSWER XZY and WZ = XZ = WX = 4 XZ XY 3 YZ therefore the triangles are similar by either SSS or SAS Similarity Theorems. WZX