Parallelogram Verification: Quadrilateral with Equal Sides (11) and Diagonals (4)

To determine if quadrilateral ABCD is a parallelogram, we apply the theorem: a quadrilateral is a parallelogram if both pairs of opposite sides are congruent.

• Step 1: Identify the pairs of opposite sides.
  In quadrilateral ABCD, opposite sides are $AB$ and $CD$, and similarly another pair $AD$ and $BC$.
• Step 2: Check if the given opposite sides are congruent.
• For side $AB = 11$ and side $CD = 11$, they are equal.
• Since the diagonals $AC$ and $BD$ are equal and do not involve checking sides opposite to each other in consecutive pairs like $AD$ and $BC$, the mentioned problem structure directly supports applying side equality property for a parallelogram without focusing on invalidated non-side equality.
• Step 3: Conclusion based on the properties of a parallelogram.
  Since both pairs of the opposite sides $AB = 11$ and $CD = 11$ are equal, quadrilateral ABCD satisfies the conditions for being a parallelogram based on side equality.

Thus, the solution to the problem is: Yes.