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Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. EXAMPLE 1. Use the AA Similarity Postulate. Because they are both right angles, D and G are congruent.
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Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. EXAMPLE 1 Use the AA Similarity Postulate
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
b. a. ∆ABEand ∆ACD ∆SVRand ∆UVT EXAMPLE 2 Show that triangles are similar Show that the two triangles are similar.
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
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
1. ∆FGHand ∆RQS ANSWER In each triangle all three angles measure 60°, so by the AA similarity postulate, the triangles are similar ∆FGH ~ ∆QRS. for Examples 1 and 2 GUIDED PRACTICE Show that the triangles are similar. Write a similarity statement.
2. ∆CDFand ∆DEF ANSWER 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.
3. Reasoning Suppose in Example 2, part (b),SRTU. Could the triangles still be similar? Explain. ANSWER Yes; if S T, the triangles are similar by the AA Similarity Postulate. for Examples 1 and 2 GUIDED PRACTICE