Introduction:
A quadrilateral is a polygon with four sides. A parallelogram is a special type of quadrilateral where opposite sides are equal and parallel. In this response, we will explore whether a quadrilateral with equal opposite sides is always a parallelogram.

Definition of a Parallelogram:
A parallelogram is a quadrilateral with opposite sides that are equal in length and parallel to each other. Additionally, the opposite angles of a parallelogram are also equal.

Proof:
To determine whether a quadrilateral with equal opposite sides is a parallelogram, we can use the properties of parallelograms to prove or disprove its classification.

Opposite Sides:
If all opposite sides of a quadrilateral are equal, we can denote them as AB, BC, CD, and DA. Let's assume AB = CD and BC = DA.

Opposite Angles:
To prove that the quadrilateral is a parallelogram, we need to show that the opposite angles are also equal.

1. Consider angle A and angle C.
- Since AB = CD and BC = DA, we can conclude that triangle ABC is congruent to triangle CDA by the Side-Side-Side (SSS) congruence criterion.
- Therefore, angle A is congruent to angle C.

2. Similarly, consider angle B and angle D.
- Since AB = CD and BC = DA, we can conclude that triangle BCD is congruent to triangle DAB by the SSS congruence criterion.
- Therefore, angle B is congruent to angle D.

Conclusion:
By proving that opposite angles are congruent, we have shown that a quadrilateral with equal opposite sides is indeed a parallelogram. Hence, the statement is true.

Summary:
In summary, a quadrilateral with equal opposite sides is a parallelogram. The proof involves demonstrating that the opposite angles are also equal by using the congruence of triangles. This property is a defining characteristic of parallelograms.