A B C D is a parallelogram. L\ a n d\ M ...

`A B C D` is a parallelogram. `L\ a n d\ M` are points on `A B\ a n d\ D C` respectively and `A L=C M` . Prove that `L M\ a n d\ B D` bisect each other.

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A B C D is a parallelogram. L and M are points on A B and D C respectively and A L=C Mdot prove that L M and B D bisect each other.

In Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points of the sides A B\ a n d\ C D respectively. Prove that the line segments A F\ a n d\ C E trisect (divide into three equal parts) the diagonal B D .

A B C D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n d\ C D respectively. G H is any line intersecting A D ,\ E F\ a n d\ B C at G ,\ P\ a n d\ H respectively. Prove that G P=P H

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B Cdot Prove that: a r\ (\ L B C)=\ a r\ (\ M B C)

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ A B M)=a r\ (\ A C L) .

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ L O B)=a r\ (\ M O C) .

A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD C respectively, then express vec A La n d vec A M in terms of vec A Ba n d vec A D . Also, prove that vec A L+ vec A M=3/2 vec A Cdot

In a \ /_\A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ /_\L C M)=a r\ (/_\ L B M)

In a triangle \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (triangle \ L O B)=a r\ (triangle \ M O C)

In Figure, A B C D is a rectangle. B M\ a n d\ D N are perpendicular from B\ a n d\ D respectively on A C . Prove that M B C~= D N A (ii) B M=D N

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