Warm Up Solve each proportion. 1. 2. 3.

1. 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;

2. Similar Triangles Section 6-3

3. Proving Triangle Similarity

4. Therefore ∆ABC ~ ∆DEC by AA~. Example: Using the AA Similarity Postulate Explain why the triangles are similar and write a similarity statement.

5. Example: Explain why the triangles are similar and write a similarity statement. ∆ABC ~ ∆DEF by AA ~.

6. Proving Triangle Similarity

7. Example: Verifying Triangle Similarity Verify that the triangles are similar. ∆PQR and ∆STU Therefore ∆PQR ~ ∆STU by SSS ~.

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

9. Example: Finding Lengths in Similar Triangles Explain why ∆ABE ~ ∆ACD, and then find CD. ∆ABE ~ ∆ACD by AA ~.