The sides `A B\ a n d\ C D` of a parallelogram `A B C D` are bisected at `E\ a n d\ F`. Prove that `E B F D` is a parallelogram.

The sides A B and C D of a parallelogram A B C D are bisected at Ea n dF . Prove that E B F D is a parallelogram.

Two segments A C and B D bisect each other at O . Prove that A B C D is a parallelogram.

Two segments A C and B D bisect each other at O . Prove that A B C D is a parallelogram.

In a parallelogram A B C D , write the sum of angle A\ a n d\ B

A B C D is a parallelogram. A B is produced to E so that B E=A B . Prove that E D bisects B C .

A B C D is a parallelogram. A B is produced to E so that B E=A B . Prove that E D bisects B Cdot

In a parallelogram A B C D , the bisector of /_A also bisects B C at X . Prove that A D=2A B .

A B C D is a parallelogram. If A B is produced to E such that B E=A B . Prove that E D bisects B C .

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

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