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 `

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.

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 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 a trapezium ABCD, if E and F be the mid-points of diagonal AC and BD respectively. Prove that EF=1/2(AB-CD).

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 a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

In a parallelogram ABCD, E and F are the mid-points of sides BC and AD respectively. Show that the line segment BF and ED trisect the diagonal AC.

A B C D is a parallelogram X and Y are the mid-points of B C and C D respectively. Prove that a r( A X Y)=3/8a r(^(gm)A B C D) GIVEN : A parallelogram A B C D in which X and Y are the mid-points of B C and C D respectively. TO PROVE : a r( A X Y)=3/8a r(^(gm)a b c d) CONSTRUCTION : Join B Ddot

X and Y are the mid-points of the opposite sides AB and DC of a parallelogram ABCD. Prove that squareAXCY is a parallelogram.

The following figure shows a triangle ABC in which P, Q and R are mid-points of sides AB, BC and CA respectively. S is mid-point of PO. Prove that : ar.(DeltaABC)=8xxar.(DeltaQSB)