The points P and S are on the same side of the line segment QR, such that ∠PQR…
2024
The points P and S are on the same side of the line segment QR, such that ∠PQR = 90°, ∠SRQ = 90° and PQ = SR. Select the correct statement.
- A.
ΔPQR ≅ ΔSRQ by RHS
- B.
ΔPQR ≅ ΔSQR by SAS
- C.
ΔPQR ≅ ΔSQR by RHS
- D.
ΔPQR ≅ ΔSRQ by SAS
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Correct answer: D
To determine the correct congruence statement for the triangles PQR and SRQ, we need to analyze the given geometric conditions carefully.
Analysis of Conditions
Given:
∠PQR = 90°
∠SRQ = 90°
PQ = SR
Shared Side:
Both triangles PQR and SRQ share the side QR.
Establishing Congruence
If we examine triangle PQR and triangle SRQ:
Side PQ = Side SR (Given)
Angle PQR = Angle SRQ = 90° (Given)
Side QR = Side QR (Common side)
By the SAS (Side-Angle-Side) congruence criterion, we have two sides and the included angle equal:
PQ = SR
∠PQR = ∠SRQ
QR = RQ
Therefore, ΔPQR ≅ ΔSRQ by the SAS criterion.