ABCD is a parallelogram. P and Q are the mid-points of sides AB and AD reapectively.
Prove that area of triangle APQ= `(1)/(8)` of the area of parallelogram ABCD.

In the figure, the area of parallelogram ABCD is

Given a parallelogram ABCD where X and Y are the mid-points of the sides BC and CD respectively . Prove that: ar (Delta AXY) = (3)/(8) xx ar (//gm) ABCD

E, F, G and H are the mid-points of the sides of a parallelogram ABCD. Show that area of quadrilateral EFGH is half of the area of parallelogram ABCD.

ABCD is a parallelogram E is mid-point of AB and DE bisects angle D. Prove that CE bisects angle C

ABCD is a parallelogram E is mid-point of AB and DE bisects angle D. Prove that angleDEC= 90^(@)

ABCD is a parallelogram. Two points P and Q are taken on sides AD and BC respectively such that AP 1/3ADand CQ=1/3BC. Prove that square AQCP is a parallelogram.

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: BDEF is a parallelogram.

In parallelogram ABCD, X and Y are mid-points of opposite sides AB and DC respectively. Prove that: (i) AX=YC. (ii) AX is parallel to YC (iii) AXCY is a parallelogram.

In the given figure, M and N are the mid-points of the sides DC and AB respectively of the parallelogram ABCD. If the area of parallelogram ABCD is 48cm^(2) , (i) State the area of the triangle BEC. (ii) name the parallelofram which is equal in area to the triangle BEC.