Question

in the given figure ,OA×OB=OC×OD,show that <A=<C and <B=<D​

Answer 1

Step-by-step explanation:

Given : OA.OB = OC.OD

To prove : angle A = angle C and angle B = angle D

Proof :

OA . OB = OC . OD. ( Given)

So, OA = OB. ( 1 )

OC. OD

In ∆ AOD & ∆ COB,

OA = OB. ( ↑1 )

OC. OD

Angle AOD = Angle COB ( Vertically opposite angle )

∆ AOD ~ ∆ COB. ( SAS criterion )

Hence,

angle A = angle C

angle B = angle D

Answer 2

Answer:

Step-by-step explanation: