Mathematics

Mathematics

Problem

(a) In triangles PQRPQR and PRSPRS, it is given that PQ=PSPQ = PS, PRPR is common and ∠QPR=∠SPR\angle QPR = \angle SPR. Under which congruence criterion are the two triangles congruent? (b) Write any one pair of corresponding equal angles that results from this congruence.
Intuitive explanation

The key here is recognizing that you have two sides and the included angle matching between the triangles—that's the SAS (Side-Angle-Side) criterion. Since PQ=PSPQ = PS (one pair of sides), ∠QPR=∠SPR\angle QPR = \angle SPR (the angle between them), and PRPR is shared (the second pair of sides), the triangles must be congruent. Once you establish congruence, corresponding parts of congruent triangles are equal, so you can identify matching angles by tracking which vertices correspond.

Intuitive explanation

The key here is recognizing that you have two sides and the included angle matching between the triangles—that's the SAS (Side-Angle-Side) criterion. Since PQ=PSPQ = PS (one pair of sides), ∠QPR=∠SPR\angle QPR = \angle SPR (the angle between them), and PRPR is shared (the second pair of sides), the triangles must be congruent. Once you establish congruence, corresponding parts of congruent triangles are equal, so you can identify matching angles by tracking which vertices correspond.

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