Question

the diagonals ac and bd of a parallelogram abcd intersect at o. if p is the mid point of ad, prove that po parallel to ab and po=1/2 of cd​

Answer 1

Answer:

Make a mid point of BC and name it E. As we know that opposite sides of a ||gm are equal. So their mid points are also at the same distance from each other. So we can say that AP=BE.

In triangle AOP and BOE

AP=BE (proved above)

AO=BO (as o is the mid of both the diagonals AC and BD

And,angle O is common

Therefore, triangle AOP is congurent to BOE (by SAS congurency rule)

Which makes PO=OE(cpct)

Therefore PE =AB and AP=BE,which makes them parallel