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Home > GC > Chapter 10 > Lesson 10.3.1 > Problem 10-96

10-96.

For each pair of triangles below, decide if the pair is similar, congruent or neither. Justify your conclusion (such as with a similarity or congruence property like or or the reasons why the triangles cannot be similar or congruent). Assume that the diagrams are not drawn to scale.

  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.

    Is the last angle congruent? Use the Triangle Angle Sum Theorem to find out.

    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?

  1. The right triangle on the left has legs 4, and, 3. The triangle on the right has side lengths 6, 8, and 10.

    Find the missing side length. Are the side ratios equal?

  1. Two intersecting line segments with segments joining the opposite ends, create two triangles, top angle on left triangle labeled, 62 degrees, bottom angle on right triangle labeled, 62 degrees.

    What kind of angles are these?

    Arc added to left triangle, right angle, & arc added to right triangle, left angle, angles between the intersecting lines on each side.

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