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. The diagonals AC and BD of a parallelogram ABCD intersect at O. If P is the midpoint of AD, prove

that

(i) PQ || AB

(ii) PO = ½ CD

Answer:

It is given that

ABCD is a parallelogram in which diagonals AC and BD intersect each other

At the point O, P is the midpoint of AD

Join OP

To find: (i) PQ || AB (ii) PQ = ½ CD \

Proof:

(i) In parallelogram diagonals bisect each other

BO = OD

Here O is the mid-point of BD

In Δ ABD

P and O is the midpoint of AD and BD

PO || AB and PO = ½ AB ….. (1)

Hence, it is proved that PO || AB.

(ii) ABCD is a parallelogram

AB = CD ……. (2)

Using both (1) and (2)

PO = ½ CD

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