If `A D` is a median of a triangle `A B C ,\ ` then prove that triangles `A D B\ a n d\ A D C` are equal in area. If `G` is the mid-point of median `A D ,` prove that `a r\ (triangle B G C)=2\a r\ (triangle \ A G 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)

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

In a triangle ABC , E is the mid-point of median AD . Show that a r\ (B E D)=1/4a r\ (A B 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)

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)

In figure, A B C\ a n d\ B D E are two equilateral triangles such that D is the mid-point of B C . If A E intersects B C in F . Prove that: ar(triangle BFE)=2ar(triangle FED) .

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

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