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Prove certain triangles are similar by using AA, SSS, and SAS.
Use triangle similarity to solve problems.
Objectives
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There are several ways to prove certain triangles are similar. The following postulate, as well as the SSS and SAS Similarity Theorems, will be used in proofs just as SSS, SAS, ASA, HL, and AAS were used to prove triangles congruent.
73 Notes and answers REVISED.notebook
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Example 1: Using the AA Similarity Postulate
Prove the triangles are similar.
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Check It Out! Example 1
Prove the trianglesare similar.
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Example 2A: Verifying Triangle Similarity
Verify that the triangles are similar.
∆PQR and ∆STU
Therefore ∆PQR ~ ∆STU by SSS ~.
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Example 2B: Verifying Triangle Similarity
∆DEF and ∆HJKVerify that the triangles are similar.
Therefore ∆DEF ~ ∆HJK by SAS ~.
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Check It Out! Example 2
Verify that ∆TXU ~ ∆VXW.
Therefore ∆TXU ~ ∆VXW by SAS ~.
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Example 3: Finding Lengths in Similar Triangles
Prove why ∆ABE ~ ∆ACD, and then find CD.
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Check It Out! Example 3
Prove why ∆RSV ~ ∆RTU and then find RT.
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Example 4: Writing Proofs with Similar Triangles
Given: 3UT = 5RT and 3VT = 5ST
Prove: ∆UVT ~ ∆RST
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Check It Out! Example 4
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Example 5: Engineering Application
BA = BF + FA ≈ 6.3 + 17 ≈ 23.3 ft
Therefore, BA = 23.3 ft.
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Check It Out! Example 5
What if…? If AB = 4x, AC = 5x, and BF = 4, find FG.
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You learned in Chapter 2 that the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence. These properties also hold true for similarity of triangles.
Oct 1710:03 PM
Assignment(p. 486) 1519, 23, 24, 30