Question

Given: S is the midpoint of QR, QR ⊥PS and RSP and QSP are right angles

Prove: PR is congruent to PQ

Answer 1

Hence proved that PR ≅ PQ.

Step-by-step explanation:

Given,

S being the midpoint of QR

SR = QS            (∵ midpoint)

PS = PS  (common side/reflexive property)

Two right triangles are congruent due to

∵ PS ≅ PS                       (SAS congruency)

QS ≅ PS

Thus, ∆RSP ≈ ∆QSP through SAS congruency.

While PQ = PR               (by CPCT).

Hence, proved.

Learn more: Prove that angles are congruent

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