Question

The figure shows triangle POR and line segment AB, which is parallel to QR:

А - В
o
R
Part A: Is triangle POR similar to triangle PAB? Explain using what you know about triangle similarity (5 points)
Part B: Which line segment on triangle PAB corresponds to line segment QR? Explain your answer. (3 points)
Part C: Which angle on triangle PAB corresponds to angle Q? Explain your answer. (2 points)

Answer 1

A: the triangles are similar

B: AB corresponds to QR

C: ∠PAB corresponds to angle Q

Explanation:

A line segment parallel to the base of a triangle will create a similar triangle. The AA similarity postulate can be used to conclude that.

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Part A:

The triangles PQR and PAB are similar. This derives from the fact that angle P is in both triangles, and corresponding angles PAB and PQR are congruent. The AA congruence postulate applies.

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Part B:

Based on the similarity statement, segment AB corresponds to segment QR.

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Part C:

Transversal PQ crosses parallel lines AB and QR at points A and Q, respectively. The corresponding angles are PAB and PQR.