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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.
Solution
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).
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