In Figure, `X ,Y` are the mid-points of opposite sides `A B` and `D C` of a parallelogram `A B C Ddot A Y` and `D X` are joined intersecting in`P ; C X` and `B Y` are joined intersecting in `Qdot` Show that DXBY is a parallelogram, ` P X Q Y` is parallelogram.

In Figure, X ,\ Y are the mid-points of opposite sides A B\ a n d\ D C of a parallelogram A B C D. A 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 (i) A X C Y is a parallelogram (ii) D X B Y\ is a parallelogram (iii) P X Q Y is a parallelogram

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

P and Q are the mid-point of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PQRS is a parallelogram.

In Figure, X ,\ Y\ are two points on equal sides A B\ a n d\ A C of a A B C such that A X=A Ydot Prove that X C=Y B

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. Compute the values of x\ a n d\ y

In Figure, A N and C P are perpendicular to the diagonal B D of a parallelogram A B C Ddot Prove that : A D N~= C B P (ii) A N=C P

E , F , G , H are respectively, the mid-points of the sides A B ,B C ,C D and D A of parallelogram A B C D . Show that the quadrilateral E F G H is a parallelogram and that its area is half the area of the parallelogram, A B C Ddot

P\ a n d\ Q are the points of trisection of the diagonal B D of a parallelogram A B C Ddot Prove that C Q is parallel to A Pdot Prove also that A C bisects P Q

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