Short Answer 
The parallelogram side theorem establishes that opposite sides in a parallelogram are equal and parallel. By analyzing the angles and using the ASA congruency criteria, it’s confirmed that triangles ABC and CDA are congruent, validating that quadrilateral ABCD meets the properties of a parallelogram.
Step 1: Understanding the Parallelogram Side Theorem
The parallelogram side theorem states that in a parallelogram, the opposite sides are both equal and parallel to each other. This property helps in determining the relationships between the sides of quadrilaterals. In our case, the quadrilateral ABCD must have its opposite sides, AB and CD, and BC and DA, satisfying this theorem for it to be classified as a parallelogram.
Step 2: Identifying Angles and Their Properties
Within parallelogram ABCD, it is critical to observe the angles formed by the sides. The angles BAC and DCA are classified as alternate interior angles, meaning they are formed when a transversal crosses parallel lines. The pairs of parallel sides, AB||CD and BC||DA, ensure that other pairs of angles, BCA and DAC, also share the same alternate interior angle property, further reinforcing the connections among the angles in the parallelogram.
Step 3: Proving Congruency and Side Lengths
To establish the congruency of triangles ABC and CDA, we can apply the ASA congruency criteria, which incorporates the angle-side-angle configuration. Given that angles BAC and DCA are equal, angles BCA and DAC are equal, and AC is a common side, we conclude:
- AB = CD (from congruency)
- BC = DA (from congruency)
This confirmation of side lengths complies with the properties of parallelograms, thereby validating that ABCD is indeed a parallelogram.