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15. Di,agonals AC and BD of a quadrilateral ABCD intersect at0 in such a way that ar(AOD) = ar(BOC). Prove thatABCD is a trapezium.

Harshit Singh , 4 Years ago
Grade 12th pass
anser 1 Answers
Pawan Prajapati

Last Activity: 4 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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