Area of the equilateral triangle:
Given : D, E, F are the mind points of BC, CA, AB.R.T.P. : We have to determine the ratio of the area of of triangle DEF and triangle ABC.Proof : F is the mid point of AB.D is the mid point of BC.
FD||AC => FD||AE
Similarly ED||AFFE||BD AFDE is a parallelogram.∠A = ∠D (Opposite angles in a parallelogram)
Similarly BDEF is a parallelogram.∠B = ∠E
In ΔABC, ΔDEF
∠A =∠D proved
∠B =∠E proved
ΔABC ~ ΔDEF (A. A similarity)
Ratio of the areas of triangle DEF and triangle ABC = 1 : 4