Question

AD is a median of a ΔABC.P is any point on AD. Show that the area of ΔABP is equal to the area of ΔACP.

Answer 1

AD is the median of ΔABC, so, it will divide ΔABC into two triangles of equal areas.
Therefore, Area(ΔABD) = area(ΔACD) ...(1)
Now PD is the median of ΔPBC.
Therefore, Area(ΔPBD) = area(ΔPCD) ...(2)
Subtract equation (2) from equation (1), we have
Area(ΔABD) - area(ΔPBD) = Area(ΔACD) - Area(ΔPCD)
Area(ΔABP) = area(ΔACP).