A trapezium is a plane figure, bounded by four straight lines. One pair of these lines is parallel, the other pair is not.
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trapezoid
The only real characteristic of a trapezoid is that one pair of opposite sides is parallel. For an isosceles trapezoid, in addition to one pair of opposite sides being parallel; the legs are congruent; each pair of base angles is congruent; and the diagonals are congruent.
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.