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Congruencies and Proportions in Similar Triangles

Lesson 8.4. Congruencies and Proportions in Similar Triangles. 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.

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Congruencies and Proportions in Similar Triangles

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  1. Lesson 8.4 Congruencies and Proportions in Similar Triangles

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

  3. A B D E C Given: BD║ CE Prove: AB · CE = AC · BD Since BE 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

  4. 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 15 ft. x ft. 9 ft. 2.5 ft.

  5. Set up proportions: • Corresponding parts (height to height, shadow to shadow) OR • Actual to shadow or = = Which one will you use? Solve. The bunny is about 3.26 ft tall.

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