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\ ( B G C)=2a r\ (\ A G C)`

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

In A 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 Pdot Prove that: a r\ (\ P R Q)=1/2a r\ (\ A R C)

In A 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 Pdot Prove that: a r\ ( R Q C)=3/8\ a r\ (\ A B C)

In A 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 Pdot Prove that: a r\ ( P B Q)=\ a r\ (\ 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 Figure, A B C\ a n d\ B D E are two equilateral triangls such that D is the mid-point of B C. If A E intersects B C in F , Prove that: a r( B D E)=1/4a r\ (\ A B C) .

The medians B E and C F of a triangle A B C intersect at G . Prove that area of triangle G B C =area of quadrilateral AGFE .