In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

The adjoining figure shows a parallelogram ABCD in which P is mid-point of AB and Q is mid-point of CD. Prove that AE=EF=FC .

ABCD is a parallelogram. E is the mid-point of AB and F is the mid-point of CD. GH is any line that intersects AD, EF and BC at G, P and H respectively. Prove that : GP=PH

In trapezium ABCD, sides AB and DC are parallel to each other. E is mid-point of AD and F is mid-point of BC. Prove that : AB + DC = 2EF.

ABCD is a parallelogram E is the mid point of AB and CE bisects angleBCD . Prove that: AE=AD?

ABCD is a parallelogram E is the mid point of AB and CE bisects angleBCD . Prove that: DE bisects angleADC

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.

ABCD is a parallelogram E is mid-point of AB and DE bisects angle D. Prove that BC= BE

ABCD is a parallelogram E is mid-point of AB and DE bisects angle D. Prove that CE bisects angle C

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.