Question

Prove that the medians of an equilateral triangles are equal

Answer 1

if the angles are equal then medians are also equal

Answer 2

Let ABC be the triangle.
draw the medians AD,BE,CF
Now,AF=FB=BD=DC=CE=EA(the bisected sides)
In ABD,and ACD which are congruent,
AD is the common side.
In ABE and CBE,
BE is the common side and the rest.
If ABC is an equilateral triangle, then ABD&ABE Should be equal.
thus ad=be=cf