Geometry

Question Analysis:
Evaluates implications of the "one pair of opposite sides" condition and common misconceptions.
The main focus is on logical deductions from the given condition and eliminating false statements.

Key Concept Explanation:
The given condition forces ABCD to be a parallelogram, but not necessarily a square (which requires all sides equal and all angles 90°).

Step-by-Step Solution:
AB ∥ CD and AB ≅ CD ⇒ ABCD is a parallelogram.
In parallelograms:
Opposite sides are parallel (A is true).
Diagonals bisect each other (D is true).
Could be a rectangle if angles are 90° (B is possible).
Squares require more conditions than given (C is false...