Question

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

Answer 1

Given :

PQRS is a square .PR and QS diagonals

bisect at O.

To prove :

ΔPOQ ≅ ΔQOR ≅ ΔROS ≅ ∆SOP

Proof :

i ) In ∆POQ , ∆QOR ,

PQ = QR [ sides of a square ]

OP = OR [ Diagonals bisect each other ]

OQ = OQ [ common ]

Therefore ,

ΔPOQ ≅ ΔQOR -----( 1 )

[ SSS congruence rule ]

ii ) In ∆POQ , ∆ROS

PQ = SR [ sides of a square ]

OP = OR

OQ = OS [ diagonals bisect each other ]

Therefore ,

ΔPOQ ≅ ΔROS -------( 2 )

[ SSS congruence rule ]

iii ) Similarly ,

ΔROS ≅ ∆SOP----( 3 )

From ( 1 ) , ( 2 ) and ( 3 ) , we get


ΔPOQ ≅ ΔQOR ≅ ΔROS ≅ ∆SOP

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