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15. Di,agonals AC and BD of a quadrilateral ABCD intersect at 0 in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium.

15. Di,agonals AC and BD of a quadrilateral ABCD intersect at
0 in such a way that ar(AOD) = ar(BOC). Prove that
ABCD is a trapezium.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
3 years ago
Adding:: ar(AOD) + ar(AOB) =ar(AOB) + ar(B()C) i"7\ ar(ADB) = ar(ACB) ...(i) A B Triangles ADB and ACB are on the same base AB and as their areas are equal, so these must be in the same parallels. .. AB JI CD. Hence, ABCD is a trapezium.

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