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9-56.

Consider the triangles at right:

  1. Are the two triangles at right similar? How do you know?

    Two triangles are similar if they have the same angle measures. Because of the Angle Sum Theorem, you only need to know two angles are congruent to know that two triangles are similar.

  2. Find the value of . Show your strategy.

    Try finding the scale factor between the two corresponding sides that are given and solve for .

    Another way to solve for is to create a proportion and cross multiply. One possible proportion is shown at right.

    cm

  3. What is the scale factor ()?

    What is the scale factor between the larger triangle and the smaller triangle? Find the ratio between corresponding sides.

  4. Find the area of each triangle.

    Use the formula for area of a triangle:

Right triangle, has a height of, x centimeters, & a base of 8 cm, with an angle of 32 degrees, across from the x side.

Right triangle, has a height of 15 cm, & a base of 24 cm, with an angle of 32 degrees, across from the 15 cm side.