`O` is any point on the diagonal `B D` of the parallelogram `A B C D`. Prove that `a r( triangle O A B)=a r(triangle O B C)`

O is any point on the diagonal B D of the parallelogram A B C D . Prove that a r( /_\O A B)=a r( /_\O B C)

In figure, A B C D is a trapezium in which A B||C D . Prove that: a r( triangle A O D)=a r( triangle B O C) .

If P is any point in the interior of a parallelogram A B C D , then prove that area of the triangle A P B is less than half the area of parallelogram.

If P is any point in the interior of a parallelogram A B C D , then prove that area of the triangle A P B is less than half the are of parallelogram.

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)

D is the mid-point of side B C of triangle A B C and E is the mid-point of B D . If O is the mid-point of A E , prove that a r(triangle B O E)=1/8a r(triangle A B C) .

A B C is a triangle in which D is the mid-point of BC and E is the mid-point of A D . Prove that area of triangle B E D=1/4area \ of triangle A B C . GIVEN : A triangle A B C ,D is the mid-point of B C and E is the mid-point of the median A D . TO PROVE : a r( triangle B E D)=1/4a r(triangle A B C)dot

Diagonals A C and B D of a quadrilateral A B C D intersect at O in such a way that a r(triangle A O D)=a r(triangle B O C) . Prove that A B C D is a trapezium.

A B C D is a trapezium with A B || D C . A line parallel to A C intersects A B at X and B C at Y . Prove that a r( triangle A D X)=a r(triangle A C Y) .

In triangle A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A P . Prove that: a r\ ( triangle R Q C)=3/8\ a r\ (triangle \ A B C) .