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class ix ncert maths..lesson 9 ..ex.9.3 q 3


AD is the median of ΔABC. Therefore, it will divide ΔABC into two triangles of equal areas.
∴ Area (ΔABD) = Area (ΔACD)
⇒  ... (1)
In ΔABD, E is the mid-point of AD. Therefore, BE is the median.
∴ Area (ΔBED) = Area (ΔABE)
⇒ Area (ΔBED) = Area (ΔABD)
⇒ Area (ΔBED) = Area (ΔABC) [From equation (1)]
⇒ Area (ΔBED) = Area (ΔABC)

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