Question

ABCD is a quadrilateral, two diagonals AC and BD intersect at point O The mid point of diagonal AC and BD are P and Q respectively, it M is the midpint of PQ show that
BA + BD = 2BD​

Answer 1

Answer:

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Class 9

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>>Mid Point Theorem

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The diagonal AC and BD of a parallelogram ABCD intersect at O. If P is the midpoint of AD, prove that PQ∥AB

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Solution

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It is given that,

ABCD is a parallelogram in which diagonals AC and BD intersect each other at int O,P is the midpoint of AD

Join OP

To prove: PQ∣∣AB

Proof:

We know that,

The diagonals of parallelogram bisect each other

⇒BO=OD

⇒O is the midpoint of BD

In △ABD

P and O is the mid point of AB and BD

⇒PO∥AB[ Converse of midpoint theorem

⇒PQ∥AB

Hence, proved