D, E and F are the mid-points of the sides BC, CA and AB, respectively of an equilateral triangle ABC. Show that D DEF is also an equilateral triangle.

Question

Philoid · Accepted Answer

Given, D, E and F are mid-points od sides BC, CA and AB, respectively.

So, EF||BC and by Mid-Point Theorem,

DF||AC and DE||AB

Also, EF = BC, DE = AB and FD = AC

Since, ABC is an equilateral triangle,

AB = BC = AC

DE = EF = FD

Thus, all sides of ΔDEF are equal.

Hence, ΔDEF is an equilateral triangle.