Line-segment AB is parallel to another line-segment \(CD\). \(O\) is the mid-point of \(AD\).
Show that
(i) \(∆AOB ≅ ∆DOC\)
(ii) \(O\) is also the mid-point of \(BC\).
Answer:
(i) Consider \(∆ AOB\) and \(∆ DOC\).
\(∠ ABO = ∠ DCO\) ( as \(AB \parallel CD\) and \(BC\) is the transversal)
\(∠ AOB = ∠ DOC\) ()
\(OA = OD\) (Given)
Therefore, \(∆AOB ≅ ∆DOC\) ()
(ii) \(OB = OC\) ()
So, \(O\) is the mid-point of \(BC\).
Hence, we proved.