In Fig.9.23, E is any point on median AD of ar Δ ABC. Show that ar (ABE) = ar (ACE).

Question

In Fig.9.23, E is any point on median AD of ar &#x394; ABC. Show that ar (ABE) = ar (ACE).

Philoid · Accepted Answer

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)

On subtracting equation (ii) from equation (i), we get,

Area (ΔABD) − Area (EBD) = Area (ΔACD) − Area (ΔECD)

Area (ΔABE) = Area (ΔACE)