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In figure (2) given below, points P and Q have been taken on opposite sides AB and CD respectively of a parallelogram ABCD such that AP = CQ. Show that AC and PQ bisect each other.

In figure (2) given below, points P and Q have been taken on opposite sides AB and CD respectively of a parallelogram ABCD such that AP = CQ. Show that AC and PQ bisect each other. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Rectilinear Figures

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Answer

Considering △AOP and △COQ we have,

⇒ ∠OAP = ∠OCQ (Alternate angles are equal)

⇒ AP = QC (Given)

⇒ ∠AOP = ∠COQ (Vertically opposite angles are equal)

Hence, △AOP ≅ △COQ by ASA axiom.

∴ AO = OC and OP = OQ (By C.P.C.T.)

Hence, proved that AC and PQ bisect each other at point O.

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