Discussion
S is a point on side QR of a triangle PQR such that \(PS \perp QR\) and PS is the bisector of \(\angle QPR\). Then, which of the following statements is true?
Answer: B
The true statement is ΔPQS ≅ ΔPRS, by ASA.
In triangles PQS and PRS:
- ∠QPS = ∠RPS, because PS bisects ∠QPR (angle);
- PS = PS, the common side (side);
- ∠PSQ = ∠PSR = 90°, because PS is perpendicular to QR (angle).
So the triangles are congruent by ASA, with P matching P, Q matching R and S matching S, which is written ΔPQS ≅ ΔPRS. RHS cannot be used because it needs the hypotenuses PQ and PR to be known equal, which is not given. Writing ΔPSR matches Q with S, the wrong correspondence.
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