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.

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

If D,E and F are the middle points of the sides BC,CA and AB of the DeltaABC , then AD+BE+CF is

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.

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 the sides of BC, CA and AB of the DeltaABC . If DeltaABC=16Sq.cm., then the area of the trapezium FBCE is-

E is the mid-point of the medium AD of the DeltaABC . Prove that DeltaBED=1/4DeltaABC .

The mid-points of the sides AB, BC and CA of the equilateral DeltaABC are D, E and F respectively, AE intersects DF at O. If angleOBD=15^@ , then angleAOB=

D and E are the mid-points of AB and AC respectively of the DeltaABC. AP is the median of BC. AP intersects DE at Q. Prove that DQ = QE and AQ = QP.

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

E is the mid-point of the side BC of the parallelogram ABCD. DE and extended AB intersects each other at F. If AB = 4 cm, then AF =