Question

Determine whether the polygons with the given vertices are congruent. Use transformations to explain your reasoning. J(1,1) K(3,2) L (4,1) and M (6,1) N (5,2) P(2,1)

Answer 1

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:

`\begin{cases}d_(jk)=d_(mn)_{} \\ \\ d_(kl)=d_(np) \\ \\ d_(cj)=d_(cj)\end{cases}`

This means that the respective segment must have the same length, now we determine those lengths:

*

`d_(jk)=\sqrt[]{(3-1)^2+(2-1)^2}\Rightarrow d_(jk)=\sqrt[]{5}`

&

`d_(mn)=\sqrt[]{(5-6)^2+(2-1)^2}\Rightarrow d_(mn)=\sqrt[]{2}`

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