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Are the Triangles Similar? Task Assessment

Mathematics Standards:

  • HSG-CO.A: Experiment with transformations in the plane
  • HSG-CO.B: Understand congruence in terms of rigid motions
1) Given Points A, B, and C are not collinear, forming angle BAC. Complete the following instructions in the applet below to make ABC and APQ:
  • Put point P on ray AB, but not between point A and B.
  • Create segment BC.
  • Put a line that passes through point P and is parallel to segment BC.
  • The line intersects ray AC at point Q.

1) Make a diagram to represent the situation described above.

2) Is segment PQ longer or shorter than segment BC?

3) Prove that △ ABC is similar to △ APQ.

4) What other pairs of segments in this figure have the same ratio of lengths that segment PQ has to segment BC (ratio PQ/BC)? Explain how you know.