Question

in quadrilateral lmno, $overline{lo}paralleloverline{mn}$. what additional information would be sufficient, along with the given, to conclude that lmno is a parallelogram? check all that apply. $squareoverline{ml}paralleloverline{no}$ $squareoverline{ml}perpoverline{lo}$ $squareoverline{lo}congoverline{mn}$ $squareoverline{ml}congoverline{lo}$ $squareoverline{mn}perpoverline{no}$

Explanation:

Step1: Recall parallelogram properties

A quadrilateral is a parallelogram if both pairs of opposite sides are parallel or if one - pair of opposite sides is both parallel and congruent.

Step2: Analyze each option

• If $\overline{ML}\parallel\overline{NO}$, then both pairs of opposite sides of quadrilateral $LMNO$ are parallel ($\overline{LO}\parallel\overline{MN}$ is given and $\overline{ML}\parallel\overline{NO}$), so it is a parallelogram.
• If $\overline{LO}\cong\overline{MN}$, and $\overline{LO}\parallel\overline{MN}$, then one - pair of opposite sides is both parallel and congruent, so it is a parallelogram.
• $\overline{ML}\perp\overline{LO}$, $\overline{ML}\cong\overline{LO}$, and $\overline{MN}\perp\overline{NO}$ do not guarantee that $LMNO$ is a parallelogram.

Answer:

$\overline{ML}\parallel\overline{NO}$, $\overline{LO}\cong\overline{MN}$