Question

The figure shows triangle ABC and line segment PQ, which is parallel to 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)

Answer 1

Answer:

For A). The ~ sign above the = sign means congruent and for a figure to be congruent it needs to be the same size but triangle APQ is smaller than triangle ABC so it would be similar, not congruent. So for answer A) the person above me(eudora) is incorect.

The correct answer to Part A would be ABC ~ APQ.

Answer 2

Answer:

A: ΔABC ≅ ΔAPQ

B: Line PQ corresponds line BC.

C: ∠APQ≅∠B

Step-by-step explanation:

In the given question line segment PQ is parallel to BC in triangle ABC.

A. Yes Δ ABC is similar to ΔAPQ.

As we know in both the triangles line PQ is parallel to BC and AB is transversal to them then ∠APQ = ∠ABC ( corresponding angles)

∠AQP=∠ACB = 90° and ∠BAC is common in both.

So all angles are same which proves ΔAPQ≅ΔABC

B: In ΔAPQ line PQ corresponds to line segment BC.

C: In ΔAPQ, ∠APQ ≅ ∠B