In Figure, `X ,Y` are the mid-points of opposite sides `A B` and `D C` of a parallelogram `A B C DdotA 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 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

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

The diagonals of a parallelogram A B C D intersect at a point Odot Through O , a line is drawn to intersect A D\ at P and B C at Qdot Show that P Q divides the parallelogram into two parts of equal area.

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

p A N D q are any two points lying on the sides D C a n d A D respectively of a parallelogram A B C Ddot Show that a r( A P B)=a r ( B Q C)dot

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 GIVEN : A quadrilateral A B C D in which L ,F ,G ,H are respectively the mid-points of the sides A B ,B C ,C D and D Adot TO PROVE : (i) Quadrilateral E F G H is a parallelogram a r(^(gm)E F G H)=1/2a r(^(gm)A B C D) CONSTRUCTION : Join A C and H F

The figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a parallelogram (b) rectangle square (d) rhombus

Show that the segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms.

The figure formed by joining the mid-point of the adjacent sides of a parallelogram is a rectangle (b) parallelogram (c) rhombus (d) square

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