Question 10 Diagonals AC and BD of a trapezium ABCD with AB ∥ DC intersect each other at O. Prove that ar (AOD) = ar (BOC). Given: A trapezium ABCD where AB ∥ DC & Diagonals AC & BD intersect each other at O. To prove: ar (AOD) = ar (BOC) Proof : ΔADC and ΔBDC lie on the same base DC and between the same parallels AB and CD. ∴ Area (ΔADC) = Area (ΔBDC) Subtracting ar(ΔDOC) both sides ⇒ Area (ΔADC) − Area (ΔDOC) = Area (ΔBDC) − Area (ΔDOC) ⇒ Area (ΔAOD) = Area (ΔBOC)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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