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CBSE Class 9 Answered

Diagonal 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.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

Given, area (AOD) = area (BOC)

area (AOD) + area (AOB) = area (BOC) + area (AOB)

area (ABD) = area (ABC)

But, triangle ABD and ABC are on the same base AB and have equal area.

They are between the same parallels

AB||DC

Hence, ABCD is a trapezium.

[Since, a pair of opposite sides is parallel]

Answered by | 04 Jun, 2014, 03:23: PM

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