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

E and F are mid-points of BC and AC

Therefore, EF = `(1)/(2)"AB"`......(i)

D and F are mid-points of AB and AC

Therefore, DF = `(1)/(2)"BC"`......(ii)
But AB = BC
From (i) and (ii)
EF = DF
Therefore, ΔDEF is an isosceles triangle.