Certainly! Let's examine each pair of quadrilaterals and determine if they can be shown to be congruent using rigid motions.
1. Quadrilateral 1 and Quadrilateral 2:
- Given the information, we can determine that quadrilateral 1 and quadrilateral 2 are not congruent.
- Therefore, we select Not congruent for this pair.
2. Quadrilateral 1 and Quadrilateral 4:
- Given the information, we can determine that quadrilateral 1 and quadrilateral 4 are not congruent.
- Therefore, we select Not congruent for this pair.
3. Quadrilateral 2 and Quadrilateral 3:
- Given the information, there is no available data to show if quadrilateral 2 and quadrilateral 3 are congruent or not.
- Therefore, for this pair, we do not have sufficient information to select either option.
4. Quadrilateral 3 and Quadrilateral 4:
- Given the information, we can determine that quadrilateral 3 and quadrilateral 4 are congruent.
- Therefore, we select Congruent for this pair.
To summarize our selections:
\begin{tabular}{|c|c|c|}
\hline & Congruent & \begin{tabular}{l}
Not \\
congruent
\end{tabular} \\
\hline \begin{tabular}{l}
quadrilateral 1 and \\
quadrilateral 2
\end{tabular} & 0 & [tex]$\bullet$[/tex] \\
\hline \begin{tabular}{l}
quadrilateral 1 and \\
quadrilateral 4
\end{tabular} & 0 & [tex]$\bullet$[/tex] \\
\hline \begin{tabular}{l}
quadrilateral 2 and \\
quadrilateral 3
\end{tabular} & 0 & - \\
\hline \begin{tabular}{l}
quadrilateral 3 and \\
quadrilateral 4
\end{tabular} & [tex]$\bullet$[/tex] & 0 \\
\hline
\end{tabular}
