If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.A.TrueB.False

Break Down the Problem

1. Identify the statement regarding the properties of a quadrilateral.
2. Determine if this property alone is sufficient to classify the shape as a parallelogram.

Relevant Concepts

1. A quadrilateral is a parallelogram if both pairs of opposite sides are parallel, or if the diagonals bisect each other.
2. The property that diagonals bisect each other is a characteristic of parallelograms.

Analysis and Detail

1. If the diagonals of a quadrilateral bisect each other, it indicates that each diagonal divides the other into two equal lengths.
2. This property is both necessary and sufficient for a quadrilateral to be classified as a parallelogram.
3. Therefore, if we observe that the diagonals bisect each other, we can conclude that the quadrilateral must be a parallelogram.

Verify and Summarize

Since the property of diagonals bisecting each other is indeed a defining trait of parallelograms, we can confidently affirm the statement.

Final Answer

A. True. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.