D and E lie on the side AB and AC of `DeltaABC` such that `DeltaDBC=DeltaEBC`, Prove that DE || BC.

In the figure D, E are points on the sides AB and AC respectively of DeltaABC such that ar(DeltaDBC) = ar(DeltaEBC) . Prove that DE || BC.

The point D and E are situated on the sides AB and AC of DeltaABC in such a way that DE||BC and AD : DB=3 :1 , If EA=3.3cm , then the length of AC is

D, E and F are the mid-points of the sides AB, BC and CA of the DeltaABC . Prove that DeltaDEF=1/4DeltaABC .

D, E and F are the mid-points of the sides AB, AC and BC of the DeltaABC. Prove that DE and AF bisects each other.

If E, F and G are the mid-points of the sides AB, BC and CA of the DeltaABC respectively, then prove that the centres of gravity of DeltaABC and DeltaEFG are the same point.

D, E and F are the mid-points of AB, BC and CA of the equilateral DeltaABC. Prove that DeltaDEF is also an equilateral triangle.

D is a point on the side BC of DeltaABC . If /_ADC=/_BAC , then prove that CA^(2)=CBxxCD .

D is any point on the side BC of the DeltaABC . P and Q are the centroids of DeltaABD and DeltaACD . Prove that PQ||BC .

DeltaABC and DeltaDBC are situated on the same base BC and on the same side of BC . E is any point on the side BC . Two line through the point E and parallel to AB and BD intersects the sides AC and DC at the points F and G respectively. Prove that AD||FG .

D and E are the mid-points of AB and AC of the equilateral DeltaABC . If DE + AB = 15 cm, then, DE =