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`

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 and A D produced at R . Prove that (i) A R=2B C (ii) B R=2B Qdot

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 R . Prove that: (i) A R=2B C (ii) B R=2\ B Q

A B C D is a parallelogram. The circle through A ,Ba n dC intersects C D produced at E , prove that A E=A Ddot

A B C D is a parallelogram. The circle through A ,Ba n dC intersects C D produced at E , prove that A E=A Ddot

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 Figure, A D is a median and B L ,\ C M are perpendiculars drawn from B\ a n d\ C respectively on A D\ a n d\ A D produced. Prove that B L=C M

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

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 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