Points P and S lie on the same side of line segment QR such that ∠PQR = 90°, ∠SRQ = 90°, and PQ = SR. Determine which congruence statement about triangles is correct.

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Accepted Answer

Given: ∠PQR = 90° and ∠SRQ = 90°, so both these angles are right angles.

Also, PQ = SR (given).

Consider triangles PQR and SRQ:
- QR is common to both triangles.
- ∠PQR = ∠SRQ = 90° (right angles).
- PQ = SR (given).

So, in triangles PQR and SRQ, we have:
- One side PQ = SR
- Included angle ∠PQR = ∠SRQ = 90°
- Side QR common

This satisfies the SAS (Side-Angle-Side) congruence criterion.

Hence, ∆PQR ≅ ∆SRQ by SAS.

The other options are incorrect because:
- RHS (Right angle-Hypotenuse-Side) requires the hypotenuse and one side equal, but here the hypotenuse is not clearly identified or equal.
- The triangles involving SQR do not satisfy the given conditions for congruence.

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