Some textbooks define a trapezoid as a quadrilateral with exactly one pair of parallel sides, while other textbooks say that a trapezoid has at least one pair of parallel sides. a. What are the consequences of choosing one of these definitions over the other? Which is correct? b. Is a parallelogram a trapezoid? Why or why not?
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Open question
2022-08-16
a. What are the consequences of choosing one of these definitions over the other? Which is correct?
b. Is a parallelogram a trapezoid? Why or why not?
Answer & Explanation
peculiopy
Beginner2022-08-17Added 8 answers
(a) If we choose the definition, that quadrilateral with exactly one pair of parallel sides ,then other two sides must be antiparallel. Normally, we use such diagram to represent a trapezoid, in which exactly one pair are parallel. With this definition, a square, rectangle, parallelogram and rhombus can not be considered as trapezoid.
When we choose the definition, trapezoid has at least one pair of parallel sides, which includes all trapezoids as defined in the first definition, as well as square, rectangle, parallelogram, and rhombus.
The second definition is more accurate because it includes more geometrical structures, and the same trapezoid formula can be used for those structures.
(b) A parallelogram is a trapezoid because it has at least one parallel pair. In fact, all parallelograms are trapezoids because both pairs of sides are parallel.
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