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Home > GC > Chapter 6 > Lesson 6.2.4 > Problem 6-72

6-72.

Examine the geometric relationships in each of the diagrams below. For each one, write and solve an equation to find the value of the variable. Name all geometric relationships or theorems that you use.

  1. Two adjacent angles together, form a 90 degree angle. The angle on the left is, 4 X minus 2 degrees. The angle on the right is, X, degrees.

    What type of angle do these two angles sum to?

  1. A triangle with labeled interior angles: top angle is 2 M + 3 degrees, lower left angle is M + 9 degrees, and lower right angle M minus 1 degrees.

    What do all the angles of a triangle sum to?

  1. 2 intersecting lines. About the point of intersection, opposite angles are 3 K, +, 18 degrees, and 7 K minus 6 degrees.

    How do these angles relate to each other?

  1. A triangle has an internal line segment parallel to the left side and stretching between the other two sides.  The two triangles share a common vertex. The diagonal side of the original triangle is 16, but, x, for the internal triangle. The base of the original triangle is 13, but, 8, for the internal triangle.

    These triangles are similar by .
    Since the triangles are similar, the ratios of corresponding sides are equal.