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

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Professor PC Thomas Classes · Answer

$$ \frac{A O}{O C}=\frac{B O}{O D} $$ ( ∵ Given)\ $\angle A O B=\angle D O C$\ (Vertically opposite angles)\ $\Rightarrow \quad 	riangle A O B \sim 	riangle C O D$\ (By SAS criterion)\ $\Rightarrow \angle A B O=\angle C D O$\ These are alternate angles.\ $\Rightarrow A B \| C D$\ $	herefore \quad A B C D$ is a trapezium.\