Through the mid-point `M` of the side `C D` of a parallelogram `A B C D` , the line `B M` is drawn intersecting `A C` at `La n dA D` produced at `E` . Prove that `E L=2B Ldot`

Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC at L and AD produced at E . Prove that EL=2BL.

P is the mid-point of side A B of a parallelogram A B C D . A line through B parallel to P D meets D C at Q\ a n d\ A D produced at Rdot Prove that: A R=2B C (ii) B R=2\ B Q

The diagonals of a parallelogram A B C D intersect at OdotA line through O intersects A B\ at X\ a n d\ D C at Ydot Prove that O X=O Y

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

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

A B C D is a parallelogram. A D is a produced to E so that D E=D C and E C produced meets A B produced in Fdot Prove that B F=B Cdot

A B C D is a cyclic quadrilateral. A Ba n dD C are produced to meet in Edot Prove that E B C-E D Adot

In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C B D

In Figure A B C D\ a n d\ A E F D are two parallelograms. Prove that: P E=F Q

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)dot