Question

In the given figure; AD is median of ΔABC and E is any point on median AD.
Prove that Area (ΔABE) = Area (ΔACE).

Answer 1

AD is the median of ΔABC. Therefore it will divide ΔABC into two triangles of equal areas.

∴ Area (ΔABD)= Area (ΔACD)           ...(i)

ED is the median of ΔEBC
∴Area (ΔEBD)= Area (ΔECD)            ...(ii)

Subtracting equation (ii) from (i), we obtain
Area (ΔABD)- Area (ΔEBD) = Area (ΔACD)- Area (ΔECD)
Area (ΔABE) = Area (ΔACE).
Hence proved