Final answer:
The correct answer to which statement about parallelograms is always true is: (2) The diagonals bisect each other.
Step-by-step explanation:
The student's question pertains to the properties of parallelograms in geometry. The correct answer to which statement about parallelograms is always true is: (2) The diagonals bisect each other. This means that each diagonal cuts the other into two equal parts at the point of intersection. Option (1), stating that the diagonals are congruent, is not always true and is specific to rectangles, a special type of parallelogram.
Option (3), which claims that the diagonals are perpendicular, is only true for rhombuses, another special type of parallelogram. Finally, the statement that diagonals bisect their respective angles is not true for parallelograms in general but is true for kites and rhombi.
Understanding these properties is important in more advanced studies of geometry and vector mathematics, as they relate to the concepts of vector addition and subtraction, particularly when vectors are represented in a parallelogram model.