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Grade 12th pass9 grade maths

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.

Harshit Singh

5 Years agoGrade 12th pass

1 Answer

Pawan Prajapati

5 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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