The diagonal `B D` of a parallelogram `A B C D` intersects the segment `A E` at the point `F ,` where E is any point on the side `B C` . Prove that `D F*E F=F B*F Adot`

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.

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 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.

Point E\ a n d\ F lie on diagonals A C of a parallelogram A B C D such that A E=C Fdot What type of quadrilateral is B F D 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(triangle A D F)=a r( triangle D C E) .

In Figure, A B C D isa trapezium in which side A B is a parallel to side D C and E is the mid-point of side A D . If F is a point on the side B C such that the segment E F is parallel to side D C . Prove that F is the mid point of B C and E F=1/2(A B+D C) .

In Figure, A B C D isa trapezium in which side A B is a parallel to side D C and E is the mid-point of side A Ddot If F is a point on the side B C such that the segment E F is parallel to side D C . Prove that F is the mid point of B C and E F=1/2(A B+D C)dot

In A B C ,A D is the median through A and E is the mid-point of A D . B E produced meets A C in F (Figure). Prove that A F=1/3A C .

A B C D is a parallelogram. E is a point on B A such that B E=2\ E A\ a n d\ F is a point on D C such that D F=2\ F C . Prove that A E C F is a parallelogram whose area is one third of the area of parallelogram A B C D .

In Figure, D E || A C and D F || A E . Prove that (E F)/(B F)=(E C)/(B E) .