Question

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

Options

• parallelogram

• trapezium

• rectangle

• square

Answer 1

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.