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Areas of Parallelograms and Triangles
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17/07/2021 11:20 am
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Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(△AOD) = ar(△BOC). Prove that ABCD is a trapezium.
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17/07/2021 11:22 am
Given,
ar(△AOD) = ar(△BOC)
To Prove
ABCD is a trapezium.
Proof:
ar(△AOD) = ar(△BOC)
⇒ ar(△AOD) + ar(△AOB) = ar(△BOC) + ar(△AOB)
⇒ ar(△ADB) = ar(△ACB)
Areas of △ADB and △ACB are equal.
∴ they must lying between the same parallel lines.
∴ AB ∥ CD
∴ ABCD is a trapezium.