Question

in quadrilateral lmno, lo || mn. what additional information would be sufficient, along with the given, to conclude that lmno is a parallelogram? check all that apply. ml || no ml ⊥ lo lo = mn ml ≅ lo mn ⊥ no

Explanation:

Step1: Recall parallelogram properties

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

Step2: Analyze each option

• If $\overline{ML}\parallel\overline{NO}$ and we already know $\overline{LO}\parallel\overline{MN}$, then by the definition of a parallelogram (a quadrilateral with two pairs of parallel sides), $LMNO$ is a parallelogram.
• $\overline{ML}\perp\overline{LO}$ only gives information about the angle between two adjacent sides and is not sufficient to prove it's a parallelogram.
• $\overline{LO}=\overline{MN}$ alone is not enough. We need information about parallelism or more congruence - relationships of opposite sides.
• $\overline{ML}\cong\overline{LO}$ gives information about adjacent sides and is not relevant to proving it's a parallelogram.
• $\overline{MN}\perp\overline{NO}$ only gives information about the angle between two adjacent sides and is not sufficient to prove it's a parallelogram.

Answer:

$\overline{ML}\parallel\overline{NO}$