The polygon is similar since the corresponding angles are congruent and the corresponding sides are proportional.
[tex]\begin{gathered} \angle G\cong\angle K \\ \angle H\cong\angle L \\ \angle J\cong\angle N \\ \angle I\cong\angle M \end{gathered}[/tex]
and
[tex]\frac{GH}{JI}=\frac{KL}{NM}[/tex][tex]\frac{GJ}{KN}=\frac{HI}{LM}[/tex]
