`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.

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 C M)=a r\ ( L B M)

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 Cdot Prove that: a r\ (\ L O B)=a r\ (\ M O C)

In a parallelogram A B C D , write the sum of angle A\ a n d\ B

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 ( A B M)=a r ( A C L)

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

A B C D is a square E ,\ F ,\ G\ a n d\ H are points on A B ,\ B C ,\ C D\ a n d\ D A respectively, such that A E=B F=C G=D Hdot Prove that E F G H is square.

A B C D is a parallelogram and E\ a n d\ F are the centroids of triangles A B D\ a n d\ B C D respectively, then E F= (a) A E (b) B E (c) C E (d) D E