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)`.

Diagonals A C and B D of a trapezium A B C D with A B || C D intersect each other at O . Prove that ar ( triangle A O D)=a r( triangle B O C) .

In Figure, A B C D is a trapezium in which A B||D C .\ \ D C is produced to E such that C E=A B , prove that a r(triangle A B D)=a r (triangle B C E) . Construction: Draw D M\ on B A produced and B N_|_D C

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)

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.

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)

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) .

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 P B Q)=\ a r\ (triangle \ A R C)

A quadrilateral A B C D is such that diagonal B D divides its area in two equal parts. Prove that B D bisects A C GIVEN : A quadrilateral A B C D in which diagonal B D bisects it. i.e. a r( triangle A B D)=a r( triangle B D C) CONSTRUCTION : Join A C Suppose A C and B D intersect at O . Draw A L_|_B D . TO PROVE : A O=O C

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 \ P R Q)=1/2a r\ (triangle \ A R C) .