Verify Parallelogram Properties: Quadrilateral ABCD with Sides 10 and 8

The problem requires us to determine if the quadrilateral ABCD is a parallelogram based on given side and diagonal lengths.

To determine if ABCD is a parallelogram, we check if both pairs of opposite sides are equal:

• For sides $AB$ and $CD$, the lengths given are $AB = 10$ and $CD = 8$. These are not equal, hence the first condition $AB = CD$ for a parallelogram is not met.
• We also need to check if the other pair of opposite sides satisfies $AD = BC$. However, without additional information, like equality of the other pair of sides, we cannot verify $AD = BC$ using the given lengths alone.

Since one necessary condition for ABCD to be a parallelogram is broken (i.e., $AB \neq CD$), we can conclude that quadrilateral ABCD is not a parallelogram.

Therefore, the correct answer is No.