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Home > GC > Chapter 7 > Lesson 7.1.3 > Problem 7-28

7-28.

Recall the three similarity shortcuts for triangles: , , and . For each pair of triangles below, decide whether the triangles are congruent and/or similar. Justify each conclusion.  

  1. Two triangles. The first triangle has sides labeled 9, 8 and 6. The second triangle has sides 13.5, 12 and 9.

    Compare the ratios of each of the pairs of corresponding sides of the two triangles.

  1. A triangle with a horizontal line drawn internally parallel to the base.

    The two triangles are similar. Justify this by examining the angles of each triangle.

  1. Two right triangles in different orientations, each with horizontal side labeled 6.

    There is not enough information to determine whether or not the two triangles are similar.

  1. Two triangles. The triangle on the left has a side length of 3 and 6, and one angle of 60 degrees between the two sides. The triangle on the right has a side length of 3 square root of 3 and 6, and one angle of 30 degrees between the two sides.

    Both triangles are isosceles. Use this information and the Triangle Sum Theorem to find the values of the unknown angles.

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