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The diagonals AC and BD of a quadrilater...

The diagonals AC and BD of a quadrilateral ABCD intersect at point 'O'. If BO = OD, then prove that the areas of `Delta ABC and Delta ADC` are equal

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In `square ABCD`, the diagonals AC and BD intersect at 'O' such that
`BO = OD`
Now, in `angle ABD, O` is the mid-point of BD
`:.` are of `Delta ABO = " area of " Delta ADO`
(`:.` median divides the triangle into two equal areas)...(1)
In `Delta CBD, O` is the mid-point of BD
`:.` area of `Delta CBO = " area of " Delta CDO`
(`:.` medians divides the triangle into two equal area)...(2)

Adding (1) and (2)
area of `Delta ABO + " area of " Delta CBO = " area of " Delta ADO + " area of " Delta CDO`
`rArr` area of `Delta ABC = " area of " Delta ADC`
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