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 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) .

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) .

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 \ 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)

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) .

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

In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-point of A C . Prove that D P=P C (ii) P R=1/2\ A C

P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and Ris the mid-point of AP, show that (i) a r (P R Q)=1/2a r(A R C) (ii) a r (R Q C)=3/8a r (A B C) (iii) a r (P B Q) =a r (ARC)

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot