Quadrilateral Analysis: Is ABCD with Sides 7,6 and Diagonals 3,4 a Parallelogram?

To determine if a quadrilateral is a parallelogram, we need to check if both pairs of opposite sides are congruent. Given:

• $AB = 7$ and $CD = 6$
• $AC = 4$ and $BD = 3$

Check for opposite sides:

• Compare $AB$ and $CD$: $7 \neq 6$.
• Diagonal lengths $AC$ and $BD$ are not used directly for parallelogram checks but confirm non-use in step.

Since $AB$ and $CD$ are not equal, the condition for opposite side congruence in a parallelogram is violated.

Thus, the quadrilateral is not a parallelogram.

Therefore, the solution to the problem is:

No.