Prove that the medians of an equilateral triangle are equal.

Let ABC be an equilateral triangle and let AD, BE and CF be the medians.
Since ΔABC is an equilateral triangle ∠A = ∠B = ∠C = 60°
Now in ΔADC and ΔABE,
we have  BC = AC
DC = AE
∠C = ∠A ...... (each 60°)
AC = AB
ΔADC ≅ ΔABE
AD = BE ...... (c.p.c.t.)
Similarly, we can prove that BE = CF
AD = BE = CF
Hence medians of equilateral triangle are equal.