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


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.Examine the diagram at right.  

  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.