Using the concept of slope, prove that medians of an equilateral triangle are perpendicular to the corresponding sides.

Explanation

Let each side be acm

Then` BD=DC=frac{{a}}{2}`

Because (`AD` is median to `BC`)

We have altitude of equilateral` triangle ABC=frac{sqrt{3}}{2} {a}`

(If `AD` is also an altitude apart from being median)

Also `AD=sqrt{AC^{2}-DC^{2}}=sqrt{a^{2}-frac{a^{2}}{4}} =sqrt{frac{3 a^{2}}{4}}=frac{sqrt{3}}{2} a`

therefore Median of equilateral triangle is also its altitude.