Question

1. which statements could you use to conclude that jklm is a parallelogram?

mn = kn and jn = ln
mj || lk and jm = lk
jm = lk and jk = jm

Explanation:

Step1: Recall parallelogram properties

One property is that the diagonals of a parallelogram bisect each other. If $\overline{MN}=\overline{KN}$ and $\overline{JN}=\overline{LN}$, the diagonals $\overline{MK}$ and $\overline{JL}$ bisect each other at point $N$.

Step2: Analyze other options

In the second option, the notation seems incorrect (it should be about sides and angles in a proper way related to parallelogram - here the notation is not standard for the property). In the third option, $\overline{LM}=\overline{LK}$ and $\overline{JK}=\overline{JM}$ just show equal - side relationships that do not directly imply parallelogram (they could be for an isosceles - type non - parallelogram shapes).

Answer:

$\overline{MN}=\overline{KN}$ and $\overline{JN}=\overline{LN}$