`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 ,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 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

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

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

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

Show that the segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms. GIVEN : A parallelogram A B C D,E and F are the mid-points of opposite sides A B and C D respectively. TO PROVE : a r(||^(gm)A E F D)=a r(||^(gm)E B C F) CONSTRCUTION : Join E Fdot

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

E , F , G , H are respectively, the mid-points of the sides of parallelogram A B C D . Show that the area of EFGH 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 : a r(^(gm)E F G H)=1/2a r(^(gm)A B C D) CONSTRUCTION : Join H and F