The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO=CO/DO Show that ABCD is a trapezium.

Question

KnowledgeBoat · Accepted Answer

Let ABCD be the quadrilateral where AC and BD intersect each other at O such that . From point O, Draw a line EO touching AD at E in such a way that, EO || AB. We know that, If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. In △ DAB, EO || AB ..........(1) Given, From (1) and (2), we get : We know that, If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. ∴ EO || DC. Since, EO || AB and EO || DC. ∴ AB || DC. Hence, proved that ABCD is a trapezium.

Mathematics

The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO=CO/DO Show that ABCD is a trapezium.

Triangles

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