In figure 5.40, ΔABC is an equilateral triangle. Points F,D and E are midpoints of side AB, side BC, side AC respectively. Show that ΔEFD is an equilateral triangle.

Given F, D and E are mid-point of AB, BC and AC of the equilateral ΔABC ∴ AB =BC = AC

So by mid-point theorem

Line joining mid-points of two sides of a triangle is 1/2 of the parallel third side.

∴ FE = 1/2 BC =

Similarly, DE = 1/2 AB

And FD = 1/2 AC

But AB =BC = AC

⇒ 1/2 AB = 1/2 BC = 1/2 AC

⇒ DE = FD = FE

Since all the sides are equal ΔDEF is a equilateral triangle.