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EXAMPLE 3

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.

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EXAMPLE 3

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  1. 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

  2. Both m A andm F equal = 53°, so A F. Next, compare the ratios of the lengths of the sides that include A and F. The lengths of the sides that include Aand F are proportional. 15 3 AC 3 AB 9 = = 10 2 FH 2 FG 6 ~ = = EXAMPLE 3 Use the SAS Similarity Theorem SOLUTION Shorter sides Longer sides

  3. 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 3 Use the SAS Similarity Theorem

  4. 18 9 3 CA 3 BC 5 CD 30 5 15 EC = = = = The corresponding side lengths are proportional. The included angles ACB and DCEare congruent because they are vertical angles. So, ACB ~DCE by the SAS Similarity Theorem. 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

  5. Explain how to show that the indicated triangles are similar. 3. SRT ~ PNQ ANSWER R  Nand == , therefore the triangles are similar by the SAS Similarity Theorem. 4 SR RT 3 PN NQ for Examples 3 and 4 GUIDED PRACTICE

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

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