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Home > CCG > Chapter 6 > Lesson 6.1.3 > Problem 6-23


For each pair of triangles below, decide if the pair is similar, congruent or neither. Justify your conclusion with a flowchart or the reasons why the triangles cannot be similar or congruent. Assume that the diagrams are not drawn to scale. Redraw and label the diagrams as needed.

  1. Two triangles. The first triangle has two angles 18 degrees and 140 degrees. The second triangle has two angles 18 degrees and 21 degrees.

    Each triangle has a missing angle.
    Use the Triangle Angle Sum Theorem to find the measure of the angles.

    Not similar.
    There are not three pairs of corresponding angles that are congruent.

  1. Two triangles where a side from each is parallel to the other. A transversal cuts through the parallel lines forming a side though not the same length of both triangles. The parallel side of the large triangle is 8, and 6 for the smaller triangle. The angle opposite the parallel sides is unknown. The angle opposite the transversal for both triangles is marked as the same.

    What kind of angles do parallel lines create?
    Does this make the triangles similar?