The figure shows triangle ABC and line segment PQ, which is parallel to BC:
Triangle ABC has a point P on side AB and point Q on side AC. The line PQ is parallel to the line BC.
Part A: Is triangle ABC similar to triangle APQ? Explain using what you know about triangle similarity. (5 points)
Part B: Which line segment on triangle APQ corresponds to line segment BC? Explain your answer. (3 points)
Part C: Which angle on triangle APQ corresponds to angle B? Explain your answer. (2 points)
Part A: Yes, triangle ABC is similar to triangle APQ. This is because if a line is parallel to one side of a triangle and intersects the other two sides, then the resulting segments created are proportional to the corresponding sides of the triangle. In this case, line segment PQ is parallel to BC, and it intersects the other sides of the triangle at points P and Q. Therefore, triangle APQ is similar to triangle ABC.
Part B: The line segment on triangle APQ that corresponds to line segment BC is line segment PQ. This is because they are parallel to each other and have the same length, as they are corresponding sides of similar triangles.
Part C: The angle on triangle APQ that corresponds to angle B is angle A. This is because angles that are in the same position in two similar triangles are corresponding angles. In this case, angle B and angle A are both angles opposite to the side BC in triangle ABC and triangle APQ, respectively. Therefore, angle A corresponds to angle B.