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

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KollegeApply · Accepted Answer

If the diagonals of a quadrilateral divide each other proportionally then it is a trapezium. Explanation: Let diagonals AC and BD meet at O. If (AO)/(OC) = (BO)/(OD), then by the Basic Proportionality Theorem and its converse a line through O can be shown parallel to one pair of opposite sides, which forces the other pair of opposite sides to be parallel. Hence, the quadrilateral has one pair of parallel sides a trapezium.

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