Question

which statement about the diagonals of a parallelogram is always true?

• the diagonals of a parallelogram are congruent.
• the diagonals of a parallelogram are perpendicular.
• the diagonals of a parallelogram bisect each other.
• the diagonals of a parallelogram bisect the opposite angles.

Explanation:

Analyze properties of a general parallelogram

• Diagonals are congruent: Only true for rectangles.
• Diagonals are perpendicular: Only true for rhombuses.
• Diagonals bisect each other: Always true for all parallelograms.
• Diagonals bisect opposite angles: Only true for rhombuses.

Answer:

• The diagonals of a parallelogram are congruent.
• The diagonals of a parallelogram are perpendicular.
• The diagonals of a parallelogram bisect each other. (Correct answer)
• The diagonals of a parallelogram bisect the opposite angles.