Question

Prove: In an equilateral triangle the three medians are equal.

https://media.glynlyon.com/g_geo_2012/9/q415a.gif

Answer 1

well, in an equilateral triangle, sides have equal length

since a median is a line going from one side to the opposite vertex, it follows that each median should have the same length, since the starting and ending points are equidistant from each other at every vertex.

another way to think about it is the median bisects each side into to equal parts. since these parts are equal, this means the median is perpendicular to the side.

since every median is perpendicular, and they all must travel the same height (since equilateral triangle), it would follow that all medians are also the same length.

not exactly sure how to prove that in the context of your problem, hope it helped though