In this problem, any of the provided statements could be used as a valid method to confirm that a quadrilateral is a parallelogram. However, the most common methods are:
- If the diagonals bisect each other, then the quadrilateral is a parallelogram.
- If one pair of sides is both congruent and parallel, then the quadrilateral is a parallelogram.
- If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.
- If both pairs of opposite sides are parallel, then the quadrilateral is a parallelogram.
- If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.
To identify which one was specifically used in your problem, you would need to refer back to the evidence or steps shown in that particular problem. If diagonals were shown to bisect each other, then the appropriate choice would be the first option. If one pair of sides was proven to be both congruent and parallel, then you would select the second statement, and so on for the other methods.
If you have details about the problem context or the steps taken, please provide that for a more accurate identification!
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