Question

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

Answer 1

Given a quadrilateral ABCD in which AC and BD are diagonals, which intersect each other at O. 

To Prove : ABCD is a trapezium such that AB || DC. 

Const : Draw a line OM || AB. 

Proof: In ∆ADB, we have OM || AB. Therefore, by using Basic proportionality theorem, we have

Therefore, by using converse of basic proportionality theorem, we have OM || DC But OM || AB (by construction) ⇒ AB || DC 

Hence, ABCD is a trapezium.