Question

Diagonals AC and BD of a trapezium ABCD with AB//DC intersect each other at O. Prove that area(AOB) = area(BOC)

Answer 1

In trapezium ABCD,diagonal AC and BD intersects at O.
To prove:
ar(AOB)=ar(BOC)
Proof:
since AB and CD are parallel lines,
ar(AOB)=ar(BOC) [areas of the triangles are equal if they have the same base and lie between the parallels]
Hence proved

Answer 2

In trapezium ABCD,diagonal AC and BD intersects at O.

To prove:

ar(AOB)=ar(BOC)

Proof:

since AB and CD are parallel lines,

ar(AOB)=ar(BOC) [areas of the triangles are equal if they have the same base and lie between the parallels]

Hence proved

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