Step 1: Understanding the Concept:
Geometrical isomerism (cis-trans) occurs in compounds with restricted rotation, typically due to a double bond, where each carbon of the double bond has two different substituents.
Step 2: Detailed Explanation:
\begin{itemize}
\item (A) 1-butene: CH\(_2\)=CH-CH\(_2\)CH\(_3\). One carbon of the double bond has two H atoms, so no geometrical isomerism.
\item (B) 1,2-dibromobutene: Br-CH=CBr-CH\(_2\)CH\(_3\). Both carbons of the double bond have different substituents (H and Br on one, Br and CH\(_2\)CH\(_3\) on the other), so it shows cis-trans isomerism.
\item (C) Propene: CH\(_3\)-CH=CH\(_2\). One carbon has two H atoms, so no geometrical isomerism.
\item (D) iso-butylene: (CH\(_3\))\(_2\)C=CH\(_2\). One carbon has two CH\(_3\) groups, the other has two H atoms, so no geometrical isomerism.
\end{itemize}
Step 3: Final Answer:
1,2-dibromobutene shows geometrical isomerism, option (B).