In Fig., \(OA = OB\) and \(OD = OC\). Show that
 
(i) \(∆ AOD ≅ ∆ BOC\) and
 
(ii) \(AD || BC\)
 
YCIND_241124_6816_1.png
 
Proof:
 
(i) In \(∆ AOD\) and \(∆ BOC\),
 
\(OA = OB\) [Given]
 
\(OD = OC\) [Given]
 
\(\angle AOD = \angle\) ( )
 
Thus, \(∆ AOD ≅ ∆ BOC\) (by the congruence rule),
 
Hence proved
   
(ii)  In \(\triangle AOD\) and \(\triangle BOC\), we have:
 
\(∠ OAD = ∠ OBC\) []
 
Therefore, \(AD \parallel BC\).
 
Hence, we proved.