ABC is an equilateral triangle and D, E and F are the midpoints of BC, CA and AB respectively.

Now, we have AB = BC = CA (sides of equilateral triangle are equal)

According to mid-point theorem,

DE is parallel to AB and DE = (1/2) AB

Similarly, DF is parallel to AC and DF = (1/2)AC and EF is parallel to BC and EF= (1/2)BC.

Since AB = BC = CA,

(1/2)AB = (1/2)BC = (1/2)CA

Thus, DE = EF = DF

 

Hence, DEF is an equilateral triangle(all the sides are equal)