To prove that quadrilateral ABCD is a parallelogram, we can utilize one of the properties that characterize parallelograms. The most straightforward options from your given answers are:
- Opposite sides of the figure are congruent.
- Adjacent angles of the figure are congruent.
- Adjacent sides of the figure are congruent.
- Adjacent sides of the figure are parallel.
Using the property of opposite sides being congruent:
If we can show that the opposite sides of quadrilateral ABCD are congruent, then we can conclude that ABCD is a parallelogram.
Let’s say:
- Side AB is congruent to side CD (AB ≅ CD)
- Side BC is congruent to side AD (BC ≅ AD)
According to the properties of parallelograms, if both pairs of opposite sides are congruent, then quadrilateral ABCD is a parallelogram.
Conclusion: If we can establish that opposite sides are congruent, then quadrilateral ABCD is proved to be a parallelogram.
So, from your options, the correct choice is "Opposite sides of the figure are congruent."
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