Short Answer 
The proof that quadrilateral ABCD is a parallelogram begins by establishing that AD is greater than or equal to BC. Next, it identifies alternate interior angles formed by transversal AC and confirms the congruence of triangles ABC and CDA using the SAS theorem, demonstrating that the opposite sides are equal, which fulfills the criteria for a parallelogram.
Step 1: Establish Given Information
The first step in proving that quadrilateral ABCD is a parallelogram is to establish the given conditions. According to the problem, we know that AD is greater than or equal to BC (AD ‚a• BC). This information serves as the foundation for our proof, emphasizing the relationship between the lengths of sides AD and BC.
Step 2: Analyze Alternate Interior Angles
Next, we investigate the angles formed by transversal line AC with the two pairs of parallel lines AD and BC. We identify that angle CAD and angle ACB are alternate interior angles. By the definition of alternate interior angles, if the two angles are formed by a transversal intersecting two lines, they are congruent, providing us with another crucial piece of information for our proof.
Step 3: Apply Triangle Congruence to Conclude
To conclude that ABCD is a parallelogram, we use the fact that the triangle formed by points A, B, and C is congruent to triangle formed by points C, D, and A. This can be confirmed using the SAS (Side-Angle-Side) theorem, where we have two sides and the angle between them equal. Thus, we deduce that AB is equal to CD and that the opposite sides of ABCD are congruent, fulfilling the condition of a parallelogram.