Short Answer 
A parallelogram is a quadrilateral with either both pairs of opposite sides parallel or at least one pair that is parallel and congruent. In the case of quadrilateral LMNO, since LO is parallel to MN, we need additional information about ML and NO‚ÄöAieither they must be parallel or LO must be congruent to MN‚ÄöAito confirm LMNO is a parallelogram.
Step 1: Understand the Definition of a Parallelogram
A parallelogram is defined as a quadrilateral that satisfies certain conditions. To determine if quadrilateral LMNO is a parallelogram, we need to verify if at least one of the following conditions holds true:
- Both pairs of opposite sides are parallel.
- At least one pair of opposite sides is both parallel and congruent.
By understanding these criteria, we can assess the conditions given in this problem effectively.
Step 2: Analyze the Given Information
The problem states that LO is parallel to MN (LO √¢¬a¬• MN). This condition alone suggests that there is at least one pair of parallel sides in LMNO. However, to conclude that LMNO is definitively a parallelogram, we need additional information about the other pair of sides.
- We need to explore the status of ML and NO.
- We can determine if they are either parallel or congruent.
These insights will help us identify the necessary conditions to satisfy the parallelogram criteria.
Step 3: Identify the Correct Additional Conditions
To confirm that LMNO is a parallelogram, we explore two additional conditions that will suffice: ML is parallel to NO or LO is congruent to MN. By having either of these conditions alongside the initial given (LO √¢¬a¬• MN), we will have met the criteria for a parallelogram.
- If ML is parallel to NO, then both pairs of opposite sides are parallel.
- If LO is congruent to MN, then we have one pair of opposite sides that are both parallel and congruent.
This leads us to conclude that the options (A) and (C) are indeed correct for establishing that LMNO is a parallelogram.