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Decide if each pair of triangles below is similar. If the triangles are similar, justify your conclusion by stating the similarity condition you used. Also, describe a possible sequence of transformations that would carry one onto the other. If the triangles are not similar, explain how you know they are not similar.

  1. A right triangle has an embedded right triangle such that the bases are parallel and the angles equal.

    If two of the corresponding angles are congruent, what do you know about the third pair of angles?

  1. Two equilateral triangles, one smaller than the other.

           equilateral triangles

    What are the angle measures of an equilateral triangle?

    Triangles are similar by  since all angle measures are . The triangle on the right could be transformed into the triangle on the left by translation and dilation.

  1. Two triangles.  The first triangle has sides labeled 11, 8 and 6.  The second triangle has sides labeled 15, 33 and 20.

    Write a ratio for each pair of corresponding sides.

  1. Two triangles.  The first triangle has angles labeled 60 degrees and 50 degrees.  The second triangle has angles labeled 25 degrees and 30 degrees.

    Find the measures of the unmarked angles.