The diagonals of a parallelogram bisect each other.

True

The statement diagonals of a parallelogram bisect each other is True. This means that in any parallelogram, each diagonal divides the other into two equal parts.

Explanation:

• Definition: A parallelogram is a quadrilateral with two pairs of parallel sides.
• Property: The diagonals of a parallelogram intersect at a point that divides each diagonal into two equal segments.

Proof:

1. Consider parallelogram ABCD with diagonals AC and BD intersecting at point O.
2. In triangles △AOB and △COD:
   • AB = CD (opposite sides of a parallelogram are equal).
   • ∠BAO = ∠DCO and ∠ABO = ∠CDO (alternate interior angles are equal).
3. By the ASA (Angle-Side-Angle) criterion, △AOB ≅ △COD.
4. Therefore, AO = OC and BO = OD, proving that the diagonals bisect each other.

This property is fundamental in geometry and is used in various proofs and applications involving parallelograms.