Question

diagonal AC and DB of a trapezium ABCD With AB||DC intersect each other at the point o. prove that OA.OD=OB.OC​

Answer 1

Answer:

ABCD is a trapezium with AB∥CD and diagonals AB and CD intersecting at O.

⇒ In △OAB and △OCD

⇒ ∠AOB=∠DOC [ Vertically opposite angles ]

⇒ ∠ABO=∠CDO [ Alternate angles ]

⇒ ∠BAO=∠OCD [ Alternate angles ]

∴ △OAB∼△OCD [ AAA similarity ]

We know that if triangles are similar, their corresponding sides are in proportion.

⇒

OC

OA

=

OD

OB

[henceproved]