In the adjoining figure, D is the mid-point of side AB of `Delta ABC` and P be any point on side BC. If `CQ ||PD`, then prove that:
area of `Delta BPQ = (1)/(2) xx " area of " Delta ABC`

In the adjoining figure, AD is the median of Delta ABC and X be any point on side AD. Prove that: area (Delta ABX) = " area " (Delta ACX)

In Delta ABC, D is the mid-point of AB and P is any point on BC. If CQ || PD meets AB and Q (shown in figure), then prove that ar (DeltaBPQ) = (1)/(2) ar (DeltaABC) .

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

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 mid-point of AB and P is any point on BC. If CQ parallel to PD meets AB at Q, prove that: 2 xx " area " (Delta BPQ) = " area "(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

Any point D is taken on the side BC of a Delta ABC and AD is produced to E such that AD = DE , prove that area of Delta BCE = area of Delta ABC ,

In the adjoining figure D, E and F are the mid-points of the sides BC, CA and AB respectively of Delta ABC . Prove that: (i) square BDEF is a parallelogram (ii) area of Delta DEF = (1)/(4) xx " area of " Delta ABC (iii) square BDEF = (1)/(2) xx " area of " Delta ABC

D is any point on side AC of a Delta ABC with AB = AC .Show that CD lt BD .

In the adjoning figure, D and E are the points on the sides AB and AC respectively of Delta ABC and area of Delta BCE = " area of " Delta BCD . Prove that DE ||BC