The statement that is not always true for a parallelogram is:

"Consecutive angles are congruent."

Explanation:

1. Consecutive angles are congruent: This is not always true because consecutive angles in a parallelogram are supplementary, meaning their sum is $180^\circ$, but they are not necessarily congruent. Congruent consecutive angles occur only if the parallelogram is a rectangle.

2. Opposite sides are congruent: This is always true in a parallelogram. Opposite sides are equal in length.

3. Diagonals bisect each other: This is always true for a parallelogram. The diagonals divide each other into two equal parts.

4. Opposite angles are congruent: This is always true for a parallelogram. Each pair of opposite angles is equal.

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Would you like further clarification or examples? 😊

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Here are 5 related questions:

1. What is the difference between a parallelogram and a rhombus?
2. How do the diagonals behave in a rectangle versus a general parallelogram?
3. What are the necessary and sufficient conditions for a quadrilateral to be a parallelogram?
4. Can a square be considered a parallelogram? Why or why not?
5. How can you use properties of parallelograms to solve coordinate geometry problems?

Tip: Remember, the key property of a parallelogram is parallelism of opposite sides; all other properties stem from this!