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Mathematics 23 Online
OpenStudy (123ab456c):

Which phrase best defines a trapezoid? A. congruent diagonals B. exactly one pair of parallel sides C. exactly two congruent sides D. no sides congruent

OpenStudy (alexandervonhumboldt2):

A trapezoid is a quadrilateral with two sides parallel.

OpenStudy (alexandervonhumboldt2):

https://en.wikipedia.org/wiki/Trapezoid

OpenStudy (alexandervonhumboldt2):

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OpenStudy (mathstudent55):

@AlexandervonHumboldt2 Did you actually read the wiki article whose link you provided above? According to that article, no answer from the choices is correct.

OpenStudy (alexandervonhumboldt2):

what do you mean? In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid [1] (pronounced: /ˈtɹæpəzɔɪd/)[2] in American and Canadian English but as a trapezium in English outside North America. The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides (if they are not parallel; otherwise there are two pairs of bases). A scalene trapezoid is a trapezoid with no sides of equal measure,[3] in contrast to the special cases below.`

OpenStudy (alexandervonhumboldt2):

this is what wiki says

OpenStudy (alexandervonhumboldt2):

you can see that there are 2 parallel sides , (the bases)

OpenStudy (mathstudent55):

The wiki definition of a trapezoid is a quadrilateral with "at least" one pair of parallel sides. According to the wiki definition, a parallelogram is a special case of a trapezoid. Choice B above is "exactly one pair of parallel sides" As you can see, choice B above is not following the wiki definition of a trapezoid. The wiki article later does mention the "exclusive definition" of a trapezoid as "exactly one pair of parallel sides", but it goes on to state that wiki has chosen the definition of "at least one pair of parallel sides."

OpenStudy (mathstudent55):

Typically in Geometry, the definition of a trapezoid is a quadrilateral with exactly one pair of parallel sides. Wiki states that in higher math, the preferred definition is a quadrilateral with at least one pair of parallel sides. We need to assume the question in this post is a geometry question, and we should ignore the wiki definition.

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