When can a trapezoid also be called a rhombus?
Mathematics · Middle School · Mon Jan 18 2021
Answered on
Answer: A trapezoid (or trapezium outside North America) can never also be called a rhombus, because these two shapes have distinct properties that define them which are not compatible with one another.
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. Depending on the specific definition (which can vary by region), a trapezoid may have exactly one pair of parallel sides (the exclusive definition), or at least one pair (the inclusive definition).
On the other hand, a rhombus is a special type of parallelogram in which all four sides have the same length. It is defined by its equal sides, and also has the property that opposite sides are parallel and opposite angles are equal, which means it always has two pairs of parallel sides.
Therefore, because a rhombus has two pairs of parallel sides, and a trapezoid generally has only one pair of parallel sides, a shape cannot be both a trapezoid and a rhombus.