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प्रश्न
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.
बेरीज
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उत्तर
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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