Question

D, E, and F are the mid-points of the sides AB, BC and CA of an isosceles ΔABC in which AB = BC.

Prove that ΔDEF is also isosceles.

Answer 1

DF = `1/2`BC          ...(i)

DE = `1/2`AC        ...(ii)

EF = `1/2`AB       

EF = `1/2`BC        ...(iii)       ...[AB = BC]

From equation (i) & (ii)

DF = EF

Hence, DEF is also isosceles triangle.