Question

Show that a median of a triangle divides it into two triangles of equal areas.

Answer 1

Let ABC be a triangle and let AD be one of its medians

We need to show that ar ($△$ABD) = ar ($△$ACD).

Since the formula for area involves altitude, let us draw AN perpendicular to BC.

Now ar($△$ABD) = $\frac{1}{2}$ × base × altitude (of triangle $△$ABD)

=$\frac{1}{2}$ × BD × AN

=$\frac{1}{2}$ × CD × AN (As BD = CD)

=$\frac{1}{2}$ × base × altitude (of $△$ACD)

= ar($△$ACD)

Hence proved that the median of a triangle divides it into 2 equal halves.