In Figure, `A B C D` is a parallelogram and `X\ a n d\ Y` are points on the diagonal `B D` such that `D X=B Y` . Prove that `A X C Y` is a parallelogram (ii) `A X=C Y ,\ A Y=C X` ` A Y B\ ~= C X D` (iv) ` A X D~=\ C Y B`

In Figure, A B C D is a parallelogram. Compute the values of x\ a n d\ y

In a A B C median A D is produced to X such that A D=D X . Prove that A B X C is a parallelogram.

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. Figure

A B C D is a parallelogram and line segments A X ,\ C Y bisect the angles A\ a n d\ C , respectively. Show that A X||C Y

In Figure, X ,\ Y are the mid-points of opposite sides A B\ a n d\ D C of a parallelogram A B C DdotA Y\ a n d\ D X are joined intersecting in P ; C X\ a n d\ B Y are joined intersecting in Q . Show that A X C Y is a parallelogram (ii) D X B Y\ is a parallelogram quadrilateral P X Q Y is a parallelogram

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

The diagonals of a parallelogram A B C D intersect at OdotA line through O intersects A B\ at X\ a n d\ D C at Ydot Prove that O X=O Y

A B C D is a trapezium with A B D Cdot A line parallel to A C intersects A B at X and B C at Ydot Prove that a r( A D X)=a r( A C Y)dot

A B C D is a trapezium with A B||D C . A line parallel to A C intersects A B at X a n d B C at Ydot Prove that a r( A D X)=a r( A C Y)dot

In Fig.85, A B C D\ a n d\ A C B Ddot Find the value of x , y , zdot