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Offline Centres

The given figure shows a trapezium ABCD in which AB || CD. O is the point of intersection of diagonals AC and BD.
Which of the following relations is always true?

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Area (ΔDOC) = Area (ΔAOB)

Area (ΔACD) = Area (ΔDBC)

Area (ΔDOC) = Area (ΔBOC)

Area (ΔADC) = Area (ΔABC)

answer is A.

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Detailed Solution

As seen in the given figure, ΔACD and ΔDBC lie on the same base DC and between the same parallels AB and CD.

It is known that triangles that lie on the same base and between the same parallels are equal in area.

Thus, area (ΔACD) = area (ΔDBC)

This property will hold true for any trapezium with parallel sides AB and CD.

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