# Objective: After studying this section, you will be able to use the concept of similarity to establish the congruence of angles and the proportionality.

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Objective: After studying this section, you will be able to use the concept of similarity to establish the congruence of angles and the proportionality of segments. 8.4 Congruences and Proportions in Similar Triangles

We can prove parts of congruent triangles congruent using CPCTC. Once we have established that two triangles are similar, we can use the definition of similar polygons to prove: 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. Given: Prove: A B C D EF

Given: Prove: A B C D EF Given: Prove: A B C D EF

Given: BE ll CE Prove: A B C E D Hint: work backwards find a proportion to help find the logical steps

While strolling one morning to get a little sun, Judy noticed that a 20-m flagpole cast a 25-m shadow. Nearby was a telephone pole that cast a 35-m shadow. How tall was the telephone pole? (Hint: draw a picture)

Given: parallelogram YSTW Prove: YX S W V T

Summary: State how you can proportions can help you solve real life problems. Homework: worksheet

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