Question

If diagonals AC & BD of a trapezium ABCD with AB parallel to DC intersect each other at O, then​

Answer 1

Step-by-step explanation:

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]

I hope it will help you