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Home > CCG > Chapter 3 > Lesson 3.1.4 > Problem 3-42

3-42.

In recent lessons, you have learned that similar triangles have equal corresponding angles. Is it possible to have equal corresponding angles when the triangles do not appear to match? What if you are not given all three angle measures? Consider the two cases below.  

  1. Find the measure of the third angle in the first pair of triangles at right. Compare the two triangles. What do you notice?

    All angles in a triangle add to .

    Triangle with angles 38 degrees and 63 degrees.

    Triangle with angles 38 degrees and 79 degrees.

  2. Examine the second pair of triangles at right. Without calculating, do you know that the unmarked angles must be equal? Why or why not?

    The unmarked angles are equal. Why?

    Triangle with angles 46 degrees and 73 degrees.

    Triangle with angles 46 degrees and 73 degrees.