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Home > GC > Chapter 6 > Lesson 6.2.3 > Problem 6-61


Two parallel line segments where opposite ends are connected by line segments, 20 + x, and, 24 + x + 2, forming 2 triangles. The sides of the parallel line segments are unknown. One triangle, has sides, 20, 24, and parallel segment, unknown.  The other triangle has sides, x + 2, and, x, with the parallel segment, unknown.Examine the triangles in the diagram at right.

  1. Are the triangles similar? If you decide that they are, then justify your conclusion using a flowchart.

    There are some parallel lines in the diagram.
    Review Math Notes in Lesson 2.1.4 for help identifying the relationships between the angles lettered , , , and below.

    Two parallel line segments, H, E, and F, G,  with connecting lines, E, G, and J, H intersecting at point, Z, forming 2 triangles, H, E, Z, and Z, F, G. Side, E, Z, is 20. Side, H, Z, is 24. Side Z, F, is x + 2. And side, Z, G, is, x.  The angle opposite side, H, Z, is, a. The angle opposite the parallel side in triangle H, E, Z, is, b. The angle opposite side, x + 2, is, d. The angle opposite the parallel side in triangle F, G, Z, is, c.

  2. Solve for . Show all work.

    When two triangles are similar, the ratios of corresponding sides are equal.
    You could use a proportion.