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 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(triangle A D F)=a r( triangle D C E) .

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).

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

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)

E is the mid-point of side AB and F is the mid point of side DC of parallelogram ABCD . Prove that AEFD 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

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

Let A B C D be a parallelogram of area 124c m^2dot If E and F are the mid-points of sides A B and C D respectively, then find the area of parallelogram A E F Ddot

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: BDEF 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.