Question

which statement is always true about a parallelogram? diagonals bisect each other. diagonals are perpendicular. diagonals bisect the angles. adjacent sides are congruent.

Explanation:

To determine the correct statement about a parallelogram, we analyze each option:

• Diagonals bisect each other: By the definition and properties of a parallelogram, the diagonals of a parallelogram always bisect each other. This is a fundamental property of parallelograms.
• Diagonals are perpendicular: This is a property of rhombuses (a special type of parallelogram), not all parallelograms. For example, a rectangle (a parallelogram) has diagonals that are equal in length but not perpendicular.
• Diagonals bisect the angles: This is a property of rhombuses, not all parallelograms. In a rectangle, the diagonals do not bisect the angles (except in the case of a square, which is a special rectangle and rhombus).
• Adjacent sides are congruent: This is a property of rhombuses (and squares), not all parallelograms. In a rectangle (a parallelogram), adjacent sides are not congruent (unless it is a square).

Answer:

A. Diagonals bisect each other.