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Prove that a median divides a triangle into two triangles of equal area.

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Best answer

Consider △ ABD

We know that

Area of △ ABD = ½ × BD × AE

In the same way

Area of △ ADC = ½ × DC × AE

From the figure we know that D is the median

So we get

BD = DC

We know that

Area of △ ABD = ½ × BD × AE

It can be written as

Area of △ ABD = ½ × DC × AE

So we get

Area of △ ABD = Area of △ ADC

Therefore, it is proved that a median divides a triangle into two triangles of equal area.

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