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


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

  1. Two triangles.  The first triangle has sides labeled 9, 8 and 6.  The second triangle has sided 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 base length of 9. The bottom left vertex angle is 72 degrees. The two other sides have one tick mark. The triangle on the right has a base length of 9 and the angle opposite is 36 degrees. The sides adjacent to the 36 degree angle each have 2 tick marks.

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