Question

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

Answer 1

Answer:

Given: △ABCD is a trapezium with AB || CD and the diagonals AC and BD

intersect at ‘0'.

To prove: OA/OC = OB/OD

Proof:

In the figure consider the triangle OAB and OCD

∠DOC = ∠AOB (Vertically opposite angles are equal)

since AB || DC,

∠DOC = ∠OAB (Alternate angles are equal)

∴ By AA corollary of similar triangles.

∴ △OAB ~ △OCB When the two triangle are similar, the side are proportionally.

⇒ OA/OC = OB/OD

Hence proved