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 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 a parallelogram ABCD, AX and CY are the bisectors of angleAandangleC respectively. Prove that AX"||"CY.

In a parallelogram ABCD, AX and CY are the bisectors of angleAandangleC respectively. Prove that AX"||"CY.

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

In Figure, A B C D is a parallelogram and X ,Y are the mid-points of sides A B and D C respectively. Show that A X C Y is a parallelogram.

In parallelogram ABCD, E is the mid-point of side AB and CE bisect angle BCD. Prove that : (i) AE=AD (ii) DE bisect angleADC and (iii) Angle DEC is a right angle.

In triangle ABC, D and E are mid-points of sides AB and BC respectively. Also, F is a point in side AC so that DF is parallel to BC (i) Prove that DBEF is a parallelogram.

ABCD is parallelogram. X and Y are the mid-points of BC and CD respectively. Prove that ar (DeltaAXY) =3/8 ar (||)^(gm) ABCD .

ABCD is parallelogram. X and Y are the mid-points of BC and CD respectively. Prove that ar (DeltaAXY) =3/8 ar (||gm ABCD) .