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Question

The diagonals of a quadrilateral ABCD intersect each other at the point O such that ΔAOBΔBOC = ΔAODΔDOC then ABCD is a ......... .

A
Parallelogram
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B
Trapezium
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C
Square
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D
All of These
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Solution

The correct option is D All of These
If the trapezium is divided into four triangles by its diagonals AC and BD (as shown on the right), intersecting at O, then the area of AOD is equal to that of BOC, and the product of the areas of AOD and BOC is equal to that of AOB and COD. The ratio of the areas of each pair of adjacent triangles is the same as that between the lengths of the parallel sides
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