A trapezoid is classed as a quadrilateral because it has 4 sides
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A trapezoid is a 4 sided quadrilateral that has a pair of opposite parallel sides of different lengths and it can also be classified as an isosceles trapezoid when it has one line of symmetry
No. There are other options. A parallelogram is a special case of a trapezoid; a trapezoid has a set of parallel sides. It is of course quite possible to draw a quadrilateral that has NO parallel sides.
No, not every trapezoid is an isosceles trapezoid.
The altitude of a trapezoid bisects the bases of the trapezoid.
All the names to classify a trapezoid are a trapezoid and a quadrilateral.