Mathematics
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
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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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