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 Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points of the sides A B\ a n d\ C D respectively. Prove that the line segments A F\ a n d\ C E trisect (divide into three equal parts) the diagonal B D .

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

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

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

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( A D F)=a r( D C E)dot

D,E and F are respectively the mid-points of the sides BC,CA and AB of a /_ABC. Show that (i) BDEF is a parallelogram

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR B A C D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

A B C D is a parallelogram. L\ a n d\ M are points on A B\ a n d\ D C respectively and A L=C M . Prove that L M\ a n d\ B D bisect each other.

In Figure, A B C D is a parallelogram and /_D A B=60^0dot If the bisectors A P\ a n d\ B P of angles A\ a n d\ B respectively, meet at P on C D , prove that P is the mid-point of C D