Quadrilateral Analysis: Testing Parallelogram Properties with Side Lengths 7, 6, 2, and 3

To determine if the quadrilateral $ABCD$ is a parallelogram, we need to check if both pairs of opposite sides are equal in length.

• Step 1: Compare opposite sides - We know $AB = 7$ and $CD = 6$. Since $AB \neq CD$, one pair of opposite sides is not equal.
• Step 2: Check potential diagonal properties - The diagonals $BD = 2$ and $AC = 3$ are also not equal in length. In a parallelogram, diagonals bisect each other, so this is irrelevant as we don't have diagonal bisection condition due to lack of bisection evidence.

Since the condition for both pairs of opposite sides being equal is violated, quadrilateral $ABCD$ is not a parallelogram.

Given this analysis, the solution to the problem is: No.