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In Fig.9.23, E is any point on median A...

In Fig.9.23, E is any point on median AD of a `DeltaA B C`. Show that `a r\ (A B E)\ =\ a r\ (A C E)dot`

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We know that the median divides a triangle into two triangles of equal areas. `AD` is the median for `triangle ABC` and `ED` is the median of `triangle EBC`
Since `AD` is the median of `triangleABC`. Therefore, it will divide `triangleABC` into two triangles of equal areas.
Hence, `Area (triangleBD) = Area (triangleACD)` ... (1)
Similarly, `ED` is the median of `triangleEBC`.
Hence, `Area (triangleEBD) = Area (triangleECD)` ... (2)
Substract equation (2) from equation (1), we obtain
`ar (triangleABD) - ar (triangleEBD) = ar (triangleACD) - ar (triangleECD)`
`Area (triangleABE) = Area (triangleACE)`
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