given: quadrilateral mnol with $ \overline { mn } \cong \overline { lo } $ and $ \overline { ml } \cong \overline { no } $ prove: mnol is a parallelogram. complete the paragraph proof. we are given that $ \overline { mn } \cong \overline { lo } $ and $ \overline { ml } \cong \overline { no } $. we can draw in mo because between any two points is a line. by the reflexive property, $ \overline { mo } \cong \overline { mo } $. by sss, $ \triangle mlo \cong \triangle \square $. by cpctc, $ \angle lmo \cong \angle \square $ and $ \angle nmo \cong \angle lom $. both pairs of angles are also $ \square $, based on the definition. based on the converse of the alternate interior angles theorem, $ \overline { mn } \parallel \overline { lo } $ and $ \overline { lm } \parallel \overline { no } $. based on the definition of a parallelogram, mnol is a parallelogram.

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# Brief Explanations:
- For the first blank: Since we have $MN\cong LO$, $ML\cong NO$, and $MO\cong MO$ (reflexive property), by SSS (Side - Side - Side) congruence criterion, $\triangle MLO\cong\triangle NOM$.
- For the second blank: By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), $\angle LMO\cong\angle NOM$ (because they are corresponding angles of congruent triangles $\triangle MLO$ and $\triangle NOM$).
- For the third blank: $\angle LMO$ and $\angle NOM$ (also $\angle NMO$ and $\angle LOM$) are alternate interior angles.

# Answer:
1. $NOM$
2. $NOM$
3. alternate interior angles

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