CPM Homework Banner

Home > CCG > Chapter 3 > Lesson 3.1.2 > Problem 3-19

3-19.

The ratios Casey wrote from part (a) of problem 3-15 are common ratios between corresponding sides of the two shapes. That is, they are ratios between the matching sides of two shapes.  

  1. Look at the two similar shapes below. Which sides correspond? Write the common ratios using the side lengths.

    Two similar right triangles oriented in the same way. The right angle is lower left, both triangles have single tick marks for bottom right angles and two tick marks for the top angles. The legs for the larger triangle are 15 and 20, for the smaller triangle 6 and 8.

    The sides labeled  and are corresponding, as are the sides labeled and .

  2. Find the hypotenuse of each triangle above. Is the ratio of the hypotenuses equal to the ratios you found in part (a)?

    Refer to the Math Notes box in this lesson (3.1.2) if you need help writing common ratios.

    Use the Pythagorean Theorem to solve for the hypotenuse.

    Use this method to find the hypotenuse of the second triangle.

    Is the ratio of the hypotenuses equal to the ratios you wrote in part (a)?


    (Note: the second solution is rejected for this problem.)