A parallelogram ABCD has P the mid-point of DC and Q a midpoint of AC such that `CQ = (1)/(4) AC. PQ` produced meets BC at R. Prove that:

R is the mid-point of BC

A parallelogram ABCD has P the mid-point of DC and Q a point of AC such that CQ = (1)/(4) AC. PQ produced meets BC at R. Prove that: PR=(1)/(2)DB .

In Figure, A B C D is a parallelogram in which P is the mid-point of D C and Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C at Rdot Prove that R is a mid-point of B Cdot

In Figure, A B C D is a parallelogram in which P is the mid-point of D C\ a n d\ Q is a point on A C such that C Q=1/4A C . If P Q produced meets B C\ a t\ R , prove that R is a mid-point of B C .

In figure, P is the mid-point of B C , ,Q is the mid-point of A P , such that B Q produced meets A C at Rdot Prove that 3RA= CA

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

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that: PB=2AD

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that : BP=2AD

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that: O is mid-point of AP.

AB and CD are the parallel sides of a trapeziuml. E is the mid-point of AD. A line through E and parallel to side AB meets the line BC at point F. Prove that F is the mid-point of BC.

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