To determine the value of \( m \) that proves quadrilateral ABCD is a parallelogram, we typically need information related to the properties of a parallelogram, such as:
- Opposite sides being equal in length.
- Opposite angles being equal.
- Consecutive angles being supplementary.
- The diagonals bisecting each other.
Since I cannot see images or visual content, I recommend checking the specific relationships among the angles or sides based on the diagram you have.
If there are given expressions involving \( m \) representing angles or lengths, set them equal as necessary to match the properties mentioned above and solve for \( m \).
If you provide me with the algebraic relationships, I can help you solve for \( m \) directly!