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7-3

7-3. Triangle Similarity: AA, SSS, SAS. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Geometry. Holt Geometry. Warm Up Solve each proportion. 1. 2. 3. 4. If ∆ QRS ~ ∆ XYZ , identify the pairs of congruent angles and write 3 proportions using pairs of corresponding sides.

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7-3

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  1. 7-3 Triangle Similarity: AA, SSS, SAS Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry

  2. Warm Up Solve each proportion. 1.2.3. 4. If ∆QRS ~ ∆XYZ, identify the pairs of congruent angles and write 3 proportions using pairs of corresponding sides. x = 8 z = ±10 Q  X; R  Y; S  Z;

  3. Objectives Prove certain triangles are similar by using AA, SSS, and SAS. Use triangle similarity to solve problems.

  4. COPY THIS SLIDE: 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.

  5. Example 1: Using the AA Similarity Postulate COPY THIS SLIDE: Explain why the triangles are similar and write a similarity statement. BCA  ECD because they are vertical angles. Also, A  D because they are right angles. Therefore ∆ABC ~ ∆DEC by AA~.

  6. Check It Out! Example 1 COPY THIS SLIDE: Explain why the triangles are similar and write a similarity statement. By the Triangle Sum Theorem, (180-90-43) mC = 47o, so C F. B E because they are right angles. Therefore, ∆ABC ~ ∆DEF by AA ~.

  7. COPY THIS SLIDE:

  8. Example 2A: Verifying Triangle Similarity COPY THIS SLIDE: Verify that the triangles are similar. ∆PQR and ∆STU Therefore ∆PQR ~ ∆STU by SSS ~.

  9. Example 2B: Verifying Triangle Similarity COPY THIS SLIDE: Verify that the triangles are similar. ∆DEF and ∆HJK D  H by the Definition of Congruent Angles. Therefore ∆DEF ~ ∆HJK by SAS ~.

  10. Check It Out! Example 2 COPY THIS SLIDE: Verify that ∆TXU ~ ∆VXW. TXU VXW by the Vertical Angles Theorem. Therefore ∆TXU ~ ∆VXW by SAS ~.

  11. Classwork/Homework • 7.3 #’s: 1-6, 11-16

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