and N are the mid-points of opposite sidesAB and CD of a parallelogram

1.	and N are the mid-points of opposite sidesAB and CD of a parallelogram ABCDrespectively. AN and CM are joined and ifP and Q are the mid-points of AN and CMrespectively, prove that PMQN is aparallelogram.14. M64Mathematics-IX
Answer» Consider a parallelogram ABCD. AB = CD [ Opposite sides of parallelogram are equal] So, AM = CN and AM ll CN [ Since AB ll CD ] So, AMCN is now a parallelogram. Now, P and Q are midpoints MC ll AN , so MQ ll NP and as opposite sides of parallelogram are equal so, MQ = PN therefore PMQN is a parallelogram.

and N are the mid-points of opposite sidesAB and CD of a parallelogram ABCDrespectively. AN and CM are joined and ifP and Q are the mid-points of AN and CMrespectively, prove that PMQN is aparallelogram.14. M64Mathematics-IX

Answer»

Consider a parallelogram ABCD.

AB = CD [ Opposite sides of parallelogram are equal]

So, AM = CN and AM ll CN [ Since AB ll CD ]

So, AMCN is now a parallelogram.

Now, P and Q are midpoints

MC ll AN , so MQ ll NP

and as opposite sides of parallelogram are equal so, MQ = PN

therefore PMQN is a parallelogram.