Among the statements provided, the one that is always true for parallelograms is 2. the diagonals bisect each other.
In a parallelogram, regardless of the specific shape (whether it’s a rectangle, rhombus, or just an irregular parallelogram), the diagonals will always cross at their midpoints. This means that each diagonal divides the other into two equal parts. This property is fundamental to parallelograms and is what distinguishes them from other quadrilaterals.
To clarify the other options:
- 1. The diagonals are congruent: This is true only for specific types of parallelograms, such as rectangles and squares, but not for all parallelograms.
- 3. The diagonals are perpendicular: This is true only for rhombuses and squares, not for all parallelograms.
- 4. The diagonals bisect their respective angles: This is also true only for rhombuses and squares, not universally applicable to all parallelograms.
So, to sum it up, the correct and universally true statement regarding all parallelograms is that their diagonals bisect each other.