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Question

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. Then, point O ___.

 



A

bisects PQ

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B

is a trisection point of PQ

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C

does not bisect PQ but only lies on PQ

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D

None of these

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Solution

The correct option is A

bisects PQ


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

In ΔODP and ΔOBQ,

BOQ=POD [Vertically opposite angles]

OBQ=ODP [atternate interior angles]

and OB = OD [given]                                                                               

ΔODPΔOBQ [by ASA congruence rule]

OP=OQ [CPCT]

So, PQ is bisected at O, or O bisects PQ.
 


Mathematics

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