Question

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

Answer 1

Draw AL perpendicular to BC.
Since AD is median of ΔABC. Therefore, D is the mid-point of BC.
⇒ BD = DC
⇒ BD x AL = DC x AL   ...(multiplying by AL)

⇒ `(1)/(2)("BD" xx "AL")`

= `(1)/(2)("DC" xx "AL")`

⇒ ar(ΔABD) = ar(ΔADC).