Tell whether the following statement is true or false:

In the adjoining figure, ABCD is a trapezium in which AB || DC and its diagonals AC and BD intersect at O. Then area of triangle AOD = area of triangle BOC.

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True

False

answer is A.

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Detailed Solution

Given ABCD is a trapezium in which AB || DC and its diagonals AC and BD intersect at O.
In the adjoining figure,ABCD is a trapezium in which AB||DC and its diagonals AC and BD intersect at O. Prove that ar AOD=ar BOC.

In the adjoining figure,ABCD is a trapezium in which AB||DC and its diagonals AC and BD intersect at O. Prove that ar AOD=ar BOC.

As, triangles ADC and BDC lies on same base and between same parallels,
Area of triangle ADC = Area of triangle BDC
Removing area of triangle DOC from both,
Area of triangle ADC - Area of triangle DOC = Area of triangle BDC - Area of triangle DOC
Area of triangle AOD = Area of triangle BOC
Given statement is true.
Hence, option 1 is correct.

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