Solving Problems Using Similarity and Congruence

~adapted from Walch EducationSolving Problems Using Similarity and Congruence

Practice # 1A 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

2.6 mx

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.

Convert all measurements and solve

(1)(2.6) = (0.65)(x)

x = 4

The height of the tree is 4 meters.

Practice # 2To 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.

Determine if the triangles are similar.

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~Ms. DambrevilleThanks for Watching!!What You Need (Geneside II)FlightCrank, @ www.emusic.com. Download, play, burn MP3s @ www.emusic.com.What You Need, track 040Other399521.78 - www.emusic.com/albums/28415/