A (-1,5), B (3,1) and C (5,7) are the vertices of the `DeltaABC.` D,E and F are the midpoint of BC, CA and AB respectively. Find the area of `DeltaDEF` and show that `DeltaABC=4DeltaDEF.`

A(-1,5),B(3,1)and C(5,7) are the vertices of the DeltaABC . If D ,E and F are the mid - points of the sides overline(BC),overline(CA)andoverline(AB) respectively , find the area of DeltaDEF . Show also that , DeltaABC=4DeltaDEF .

The coordinatea of A,B and C of the DeltaABC are (3,1), (9,7) and (-3,7) respectively. If D,E and F are the mid-point of the sides bar(BC),bar(CA)andbar(AB) respectively, then find the area of the DeltaDEF. Also show that DeltaABC=4DeltaDEF.

D is the mid-point of BC of DeltaABC . E and O are the mid-points of BD and AE respectively. Then the area of the triangle BOE is-

D, E, F are mid points of sides BC, CA, AB of Delta ABC . Find the ratio of areas of Delta DEF and Delta ABC .

B is a vertex of the isosceles triangle ABC. D and E are the mid-points of AB and AC. If BE and CD intersects each other at F prove that DeltaBDE=3DeltaDEF .

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 the sides AB, BC and CA of the DeltaABC . Prove that DeltaDEF=1/4DeltaABC .

In the figure, ΔABC, D, E, F are the midpoints of sides BC, CA and AB respectively. Show that (i) BDEF is a parallelogram (ii) ar(DeltaDEF)=1/4ar(DeltaABC) (iii) ar(BDEF)=1/2ar(DeltaABC)

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.

A (2,0) B(4,4) and C (6,2) are the vetices of the triangleABC . The mid - points of bar(BC) , bar(CA) and bar(AB) are D (5,3), E(4,1) and F(3,2) respectively. Then find the length of the three medians.