parallelogram?
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A trapezoid can also take the form of an isosceles trapezoid
No, not every quadrilateral is a trapezoid, although a trapezoid is also a quadrilateral because it has four sides.
A trapezoid is called a trapezium in the UK (because the UK trapezoid is scalene). In any case, a trapezoid is also a quadrilateral, in that it has four sides.
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 is a 4 sided quadrilateral which can also take the shape of an isosceles trapezoid and in the UK it is known as a trapezium