We will determine if the polygons are congruent as follows:
First, since we are give sets of coordinates that describe each polygon, and we have that both are triangles; then in order for the triangles JKL & MNP to be congruent they have to follow:
[tex]\begin{cases}d_{jk}=d_{mn}_{} \\ \\ d_{kl}=d_{np} \\ \\ d_{cj}=d_{cj}\end{cases}[/tex]
This means that the respective segment must have the same length, now we determine those lengths:
*
[tex]d_{jk}=\sqrt[]{(3-1)^2+(2-1)^2}\Rightarrow d_{jk}=\sqrt[]{5}[/tex]
&
[tex]d_{mn}=\sqrt[]{(5-6)^2+(2-1)^2}\Rightarrow d_{mn}=\sqrt[]{2}[/tex]
From this, we can see rigth away that they are in fact not congruent.
No, they are not congruent triangle JKL is not a rigid motion of triangle MNP
