Can a trapezoid be a square?

Answer 1

Wikipedia defines a trapezium (trapezoid) as a quadrilateral with one pair of parallel sides. However, it also acknowledges that there is disagreement as to whether or not that means exactly one pair or at least one pair.

Under the first definition a trapezium could not be a square whereas under the second, it would.

Sorry not to give you an unambiguous answer but ...

Answer 2

No, a trapezoid can't be a square. A trapezoid is a quadrilateral with two parallel sides, whereas a square is a regular quadrilateral with four equal sides and four equal (right) angles, which means that opposite sides are parallel, and all sides have the same length measure. But, if you "play" with the trapezoid, you can form a square into it. For example, if the height of the trapezoid is equal in length to the length of the small base, by drawing the perpendiculars to the biggest base, you can form a square with length as the length of the small base. Or, if you have a right trapezoid, where the side that form the right angle with the biggest base has the same length as the small base has, just draw one perpendicular to the biggest base, which is parallel and equal in length to that side and the small base also. In this way you can form a square into the trapezoid, with side length as the length of the small base and the height length of the right trapezoid.