Question

Question 14
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 is its diagonals AC and BD. Show that PQ is bisected at 0.

Thinking Process

Firstly, prove that $\Delta ODPand\Delta OBQ$ are congruent by ASA rule. Further show the required result by CPCT rule.

Answer 1

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

To show PQ is bisected at O.

In $\Delta ODPand\Delta OBQ,$
$\angle BOQ=\angle POD$ [since, vertically opposite angles]

$\angle OBQ=\angle ODP$ [atternate interior angles]

and OB = OD [given]

$\therefore$ $\Delta ODP=\Delta OBQ$ [by ASA congruence rule]

$\therefore$ OP=OQ [by CPCT rule]

So, PQ is bisceted at O.