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Home > CCG > Chapter 7 > Lesson 7.3.1 > Problem 7-120

7-120.

Examine the diagram below.

Right triangle K, S, A with a vertical line segment R, H drawn perpendicular to leg S, A within the triangle. Side R, S and side K, R are both marked with one tick mark. Angle R, H, S is 90 degrees. Angle A is 90 degrees.

  1. Are the triangles in this diagram similar? Justify your answer using similarity transformations.

    Draw and separately. Which angles are congruent?

  2. What is the relationship between and ? Between and ? Between and ?

    Compare with . How are these lengths related? If the triangles are similar,
    then this relationship will be true for the other pairs of corresponding sides.

  3. If units and units, what is ?

    Add the lengths to your diagram from part (a). If , what is ?
    Use the Pythagorean Theorem to calculate the unknown side length.