![]() Substitute RS for 10, 12 for TU, 8 for SV. Therefore ∆RSV ~ ∆RTU by AA ~.Ĭheck It Out! Example 3 Continued Step 2 Find RT. Divide both sides by 9.Ĭheck It Out! Example 3 Explain why ∆RSV ~ ∆RTU and then find RT. ![]() Substitute x for CD, 5 for BE, 3 for CB, and 9 for BA. Therefore ∆ABE ~ ∆ACD by AA ~.Įxample 3 Continued Step 2 Find CD. A A by Reflexive Property of , and B C since they are both right angles. Therefore ∆TXU ~ ∆VXW by SAS ~.Įxample 3: Finding Lengths in Similar Triangles Explain why ∆ABE ~ ∆ACD, and then find CD. TXU VXW by the Vertical Angles Theorem. Therefore ∆DEF ~ ∆HJK by SAS ~.Ĭheck It Out! Example 2 Verify that ∆TXU ~ ∆VXW. ∆DEF and ∆HJK D H by the Definition of Congruent Angles. ∆PQR and ∆STU Therefore ∆PQR ~ ∆STU by SSS ~.Įxample 2B: Verifying Triangle Similarity Verify that the triangles are similar. Therefore, ∆ABC ~ ∆DEF by AA ~.Įxample 2A: Verifying Triangle Similarity Verify that the triangles are similar. B E by the Right Angle Congruence Theorem. ![]() By the Triangle Sum Theorem, mC = 47°, so C F. Example 1: Using the AA Similarity Postulate Explain why the triangles are similar and write a similarity statement.Ĭheck It Out! Example 1 Explain why the triangles are similar and write a similarity statement. Also, A D by the Right Angle Congruence Theorem. Since, B E by the Alternate Interior Angles Theorem. 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. There are several ways to prove certain triangles are similar. Use triangle similarity to solve problems. Objectives Prove certain triangles are similar by using AA, SSS, and SAS. If ∆QRS ~ ∆XYZ, identify the pairs of congruent angles and write 3 proportions using pairs of corresponding sides. Triangle Similarity: AA, SSS, SAS Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry
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