Question

A median of a triangle divides it into two ___________.

Answer 1

Let ABC be a triangle with a mid-point D on BC.
Therefore, BD = DC
Let AE be the altitude from A on BC.

Now, ar(∆ABD) = $\frac{1}{2}$× base × height
= $\frac{1}{2}$× BD × AE

Also, ar(∆ACD) = $\frac{1}{2}$× base × height
= $\frac{1}{2}$× CD × AE
= $\frac{1}{2}$× BD × AE (∵ BD = CD)
= ar(∆ABD)


Hence, a median of a triangle divides it into two triangles of equal area.