The nonparallel sides of a trapezoid are called the legs. The parallel sides are called the bases.
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There is no specific name but you could refer to them as them as the lateral sides.
A trapezoid with its nonparallel sides congruent is called an isosceles trapezoid.
The leg of a trapezoid is one of the two nonparallel sides of the trapezoid. However, the base of a trapezoid is of the two parallel sides of the trapezoid.
If the two sides which are not parallel have equal lengths, then the trapezoid is called an isosceles trapezoid (standard trapezoid has unequal sides). The base angles in an isosceles trapezoid are equal in measurement, also I know that a trapezoid with two nonparallel sides the same length is called an isosceles trapezoid.
A trapezoid can be drawn to fit the description, as a trapezoid is a quadrilateral with two sides parallel and two sides nonparallel.
The parallel sides of a trapezoid are the two bases