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Solving Problems Using Similarity and Congruence

Solving Problems Using Similarity and Congruence. ~adapted from Walch Education. Practice # 1. A meterstick casts a shadow 65 centimeters long. At the same time, a tree casts a shadow 2.6 meters long. How tall is the tree? Draw a picture. x. 2.6 m. Determine if the triangles are similar.

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Solving Problems Using Similarity and Congruence

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  1. Solving Problems Using Similarity and Congruence ~adapted from Walch Education

  2. Practice # 1 • A meterstick casts a shadow 65 centimeters long. At the same time, a tree casts a shadow 2.6 meters long. How tall is the tree? • Draw a picture x 2.6 m

  3. Determine if the triangles are similar. • The rays of the sun create the shadows, which are considered to be parallel. • Two angles of the triangles are congruent; therefore, by Angle-Angle Similarity, the triangles are similar.

  4. Convert all measurements and solve • (1)(2.6) = (0.65)(x) • x = 4 • The height of the tree is 4 meters.

  5. Practice # 2 • To find the distance across a pond, Rita climbs a 30-foot observation tower on the shore of the pond and locates points A and B so that is perpendicular to . She then finds the measure of to be 12 feet. What is the measure of , the distance across the pond? Use the diagram to find the answer.

  6. Determine if the triangles are similar.

  7. Solve the problem. • Similar triangles have proportional sides. • Create a proportion to find the distance across the pond. The distance across the pond is 75 feet. (12)(x) = (30)(30) x = 75

  8. Thanks for Watching!! ~Ms. Dambreville

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