Prove the triangles are congruent

Question

Given: PS ⟂ SQ , RQ ⟂ QS , PQ ≅ RS

Prove: △PSQ ≅ △RQS

Answer 1

PSQ and RQS are both right triangles.

PQ and RS are congruent hypotenuses.

SQ is shared by both PQS and RQS so they are congruent legs.

So PQS and RQS are congruent by HL (hypotenuse-leg).