EXAMPLE 1

1. EXAMPLE 1 Use the AA Similarity Postulate Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning.

2. Because they are both right angles, Dand Gare congruent. By the Triangle Sum Theorem, 26° + 90° +m E= 180°, so m E= 64°. Therefore, Eand Hare congruent. ANSWER So, ∆CDE~∆KGHby the AA Similarity Postulate. EXAMPLE 1 Use the AA Similarity Postulate SOLUTION

3. b. a. ∆ABEand ∆ACD ∆SVRand ∆UVT EXAMPLE 2 Show that triangles are similar Show that the two triangles are similar.

4. a. You may find it helpful to redraw the triangles separately. Because mABE and mC both equal 52°,ABEC.By the Reflexive Property, AA. ANSWER So, ∆ ABE~ ∆ ACDby the AA Similarity Postulate. EXAMPLE 2 Show that triangles are similar SOLUTION

5. b. You know SVRUVTby the Vertical Angles Congruence Theorem. The diagram shows RS||UTso SUby the Alternate Interior Angles Theorem. ANSWER So, ∆SVR~ ∆UVTby the AA Similarity Postulate. EXAMPLE 2 Show that triangles are similar SOLUTION

6. 1. ∆ FGHand ∆ RQS for Examples 1 and 2 GUIDED PRACTICE Show that the triangles are similar. Write a similarity statement. SOLUTION In each triangle all three angles measure 60°, so by the AA similarity postulate, the triangles are similar ∆FGH ~ ∆QRS.

7. 2. ∆ CDFand ∆ DEF Since m CDF = 58°by the Triangle Sum Theorem and mDFE = 90°by the Linear Pair Postulate the two triangles are similar by theAASimilarity Postulate; ∆CDF ~ ∆DEF. for Examples 1 and 2 GUIDED PRACTICE Show that the triangles are similar. Write a similarity statement. SOLUTION

8. 3. Reasoning Suppose in Example 2, part (b),SRTU. Could the triangles still be similar? Explain. Yes; if S T, the triangles are similar by the AA Similarity Postulate. for Examples 1 and 2 GUIDED PRACTICE SOLUTION