Question

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

Answer 1

ABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = ½ AN x BD [1]

ar(ACD) = ½ AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal area.