Short Answer 
To determine if a quadrilateral is a parallelogram, it must meet specific criteria such as having equal opposite sides and angles, as well as bisected diagonals. In this case, since AB is parallel to CD and their lengths are equal, quadrilateral ABCD can be concluded to be a parallelogram.
Step 1: Identify the Criteria for a Parallelogram
To determine if a quadrilateral is a *parallelogram*, certain conditions must be fulfilled. These are:
- Both pairs of opposite sides must be equal.
- Both pairs of opposite sides must be parallel.
- Opposite angles must be equal.
- Diagonals must bisect each other.
- A pair of opposite sides must be both parallel and equal.
Step 2: Use Given Information
In your scenario, you know that *AB* is parallel to *CD* (AB || CD). To prove that quadrilateral ABCD is a parallelogram, you need to either confirm that *AD* is parallel to *BC* or that the lengths of *AB* and *CD* are equal. This existing parallel condition gives one side of the argument for a parallelogram.
Step 3: Choose the Correct Option
Given that it’s confirmed *AB* = *CD*, this provides the necessary condition to conclude that ABCD is indeed a parallelogram. Therefore, the correct option to prove that quadrilateral ABCD is a parallelogram is the one indicating that *AB* = *CD*.