1. WARM UP <T = 45

2. Warm Up

3. 8.4 Congruencies and Proportions in Similar Triangles

4. If we know that two triangles are congruent, we can use the definition of congruent triangles (CPCTC) to prove that pairs of angles and sides are congruent. Likewise, if two triangles are similar, we can use the definition of similar polygons to prove that:

5. 1.Corresponding sides of the triangles are proportional. (The ratios of the measures of corresponding sides are equal) 2.Corresponding angles of the triangles are congruent. Corresponding angles of similar triangles are congruent.

6. Problem 1: Given: BD  CE Prove: AB · CE = AC · BD  A B C D E

7. A B C D E = Since BD is parallel to CE, <ABD congruent to <ACE (corr <) <ADB congruent to <AEC (corr <) ΔABD ~ΔACE (AA) Corr. Sides = ratio AB · CE = AC · BD means extremes

9. Mr. Bunny is nine feet away from a flag pole that is 15 feet high. If Mr. Bunny’s shadow is 2.5 ft long, and touches the end of the shadow of the flag pole, how tall is the bunny? HINT:draw the picture set up proportions solve

10. 15 ft. 9 ft.2.5 ft. x ft.

11. Set up proportions: Corresponding parts (height to height, shadow to shadow) Actual to shadow Corresponding parts (height to height, shadow to shadow) Actual to shadow = 11.5x = 37.5 x = 3.26 ft List the corresponding sides you are using, then solve. =