Question

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Show that OA/OC = OB/OD.

Answer 1

A trapezium ABCD with AB || DC.

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

This is referred to as AA similarity criterion for two triangles.

In ΔAOB and ΔCOD

∠AOB = ∠COD (vertically opposite angles)

∠BAO = ∠DCO (alternate interior angles)

⇒ ΔAOB ∼ ΔCOD (AA criterion)

Hence, OA/OC = OB/OD