The medians of a triangle ABC intersect each other at point G. If one of its medians is AD, Prove that :
(i) ` "Area (ΔABD)=3x "Area" (ΔBGD)`
(ii) ` "Area (ΔACD)=3x "Area" (ΔCGD)`
(iii) ` "Area (ΔBGC)=(1)/(3)x "Area" (ΔABC)`

In the given figure, the diagonals AC and BD intersects at point O. If OB=OD and AB////DC , prove that : (i) "Area" (DeltaDOC)= "Area" (DeltaAOB) . (ii) "Area" (DeltaDCB)= "Area" (DeltaACB) . (iii) ABCD is a parallelogram.

The medians of Delta ABC intersect at point G. Prove that: area of Delta AGB = (1)/(3) xx " area of " Delta ABC

The median BE and CF of a triangle ABC intersect at G. Prove that the area of DeltaGBC = area of the quadrilateral AFGE.

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 .

In the given figure, diagonals PR and QS of thr parallelogram PQRS intersect at point O and LM is parallel to PS. Show that : (i) 2 "Area" (DeltaPOS)= "Area" (////gmPMLS) (ii) "Area" (DeltaPOS)+ "Area" (DeltaQOR) =(1)/(2) "Area" (////gmPQRS) (iii) "Area" (DeltaPOS)+ "Area" (DeltaQOR) = "Area" (DeltaPOQ)+ "Area" (tDeltaSOR)

In the given figure, AD is median of DeltaABC and E is any point on median AD. Prove that Area (DeltaABE) = Area (DeltaACE)

In the figure of question 2 , if E is the mid point of median AD, then prove that : "Area" (DeltaABE)=(1)/(4) "Area" (DeltaABC) .

In the figure of question 2 , if E is the mid point of median AD, then prove that : "Area" (DeltaABE)=(1)/(4) "Area" (DeltaABC) .

D is the mid-point of side AB of the triangle ABC.E is the mid-point of CD and F is the mid-point of AE. Prove that 8 xx " area of " (DeltaAFD) = " area of " Delta ABC

In triangle ABC, D is a point in side BC such that 2BD=3DC . Prove that the area of triangle ABD = (3)/(5)xx "Area of" DeltaABC