Mathematics
P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.
Rectilinear Figures
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Answer
Parallelogram ABCD is shown in the figure below:
Considering △OAP and △OCQ we have,
⇒ ∠OAP = ∠OCQ (Alternate angles are equal)
⇒ OA = OC (As diagonals bisect each other)
⇒ ∠AOP = ∠COQ (Vertically opposite angles)
Hence, △OAP ≅ △OCQ by ASA axiom.
OP = OQ (By C.P.C.T.)
Hence, proved that PQ is bisected at O.
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In figure (1) given below, ABCD is a parallelogram and X is mid-point of BC. The line AX produced meets DC produced at Q. The parallelogram ABPQ is completed. Prove that
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