Question

Diagnals AC and BD of trapezium ABCD,with AB//CD intersect each other at point O.

prove that OA= OB ​

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.

⇒

O C

O A

=

O D

O B

[henceproved]