Q18 of 186 Page 263

If the diagonals of a quadrilateral divide each other proportionally then it is a


Given that ABCD is a quadrilateral and diagonals AC and BD intersect at O such that


IN Δ AOD and ΔBOC



∠ AOD = ∠COB


Thus Δ AOC ∼ ΔBOC (SAS similarity criterion)


⇒ ∠OAD = ∠ OCB ……………..1


Now transversal AC intersect AD and BC such the ∠CAD = ∠ACB


(from …..1 ) (alternate opposite angles)


So AD ∥ BC


Hence ABCD is a trapezium

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