Q14 of 56 Page 82

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.


Given, ABCD is a parallelogram whose diagonals bisect each other at O.


Now, in ΔODP and ΔOBQ,


∠BOQ = ∠POD


∠OBQ = ∠ODP (AD||BC and BD is transversal)


OB = OD



OP = OQ


Hence, O bisect PQ.


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