All trapezoids are parallelograms.
A. True
B. False
The correct answer and explanation is:
The correct answer is B. False.
While both trapezoids and parallelograms are types of quadrilaterals, they have different properties that make them distinct from each other.
A trapezoid is defined as a quadrilateral with exactly one pair of parallel sides. These parallel sides are called the bases, and the non-parallel sides are called the legs. The legs may or may not be equal in length. A trapezoid does not necessarily have to have opposite sides that are equal in length or parallel, which makes it fundamentally different from a parallelogram.
On the other hand, a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel and equal in length. Additionally, the opposite angles of a parallelogram are equal, and the diagonals bisect each other at their midpoints. This set of properties is stricter than that of a trapezoid, which only requires one pair of parallel sides.
Because trapezoids only have one pair of parallel sides and do not require both pairs to be parallel or equal, they cannot be considered parallelograms. All parallelograms, such as rectangles, rhombuses, and squares, have two pairs of parallel sides, which distinguishes them from trapezoids.
In summary, although both trapezoids and parallelograms are quadrilaterals, the lack of two pairs of parallel sides in a trapezoid makes it incorrect to say that all trapezoids are parallelograms. Therefore, the correct statement is B. False.