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4-42.

For each part below, decide if the triangles are similar. If they are similar, use the properties of similarity to solve for . If they are not similar, explain why not.

  1. A triangle with an internal horizontal line drawn parallel to the base forming an internal triangle sharing the top vertex. For the internal triangle, the left side is 8 and the right side is 13. For the main triangle the left side is 8 + 5 and the right side s 13 + x.

    What do the parallel lines tell you about the angles in the triangles?

  1. A transversal segment connects the ends of two parallel line segments, 5, and x. A triangle is formed when the opposite end of the parallel segment, 5, has a diagonal line segment, 8, that connects at the point where the transversal connects to the parallel segment, x. And at the end of the parallel segment, x, another diagonal line, 4, connects to a point further along on the transversal forming a second triangle.

    Can you confirm any similar angles?

    Not enough information.

  1. Two parallel line segments, length, x, and 8, have at each end, lines crisscrossing to the opposite end of the other parallel line segment forming two triangles when the lines intersect. one triangle has sides, x, 8, and unknown. The other triangle has sides 6, 8, and 4. Two of the sides, 8, and 6 are on the same line between the two triangles.

    Which angles are congruent? Which sides correspond?