Q. 23.8( 25 Votes )

# In a square PQRS, diagonals bisect each other at O. Prove that ΔPOQ ≅ ΔQOR ≅ ΔROS ≅ ΔSOP.

Answer :

In ΔPOQ, ΔQOR , ΔROS, and ΔSOP

PQ = QR = RS = SP (All sides of a square are equal)

∠POQ = ∠QOR = ∠ROS = ∠SOP = 90^{0} (Diagonals of a square bisect at right angle)

PO = QO = RO = SO (Diagonals bisect each other)

So ΔPOQ ≅ ΔQOR ≅ ΔROS ≅ ΔSOP by S.A.S. axiom of congruency

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