Question

prove that the medians of an equilateral triangle are equal

Answer 1

Consider an equilateral ΔABC. Let AD, BE and CF be the medians of BC, AC and AB respectively.
We know that in an equilateral Δ, medians are altitudes as well.
Let AB = BC = AC = x [say]
In right ΔABD, by pythagoras theorem,
AB2 = AD2 + BD2

In right ΔBEC,
BC2 = BE2 + CE2

Similarly, we can show that CF = .
Thus, AD = BE = CF.
Hence we are done.

Answer 2

here is respetive triangle..to explain in above detail.