A trapezoid is a quadrilateral with one pair of parallel sides.
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A quadrilateral that has one (and only one) pair of parallel sides is a trapezoid. It is isosceles of the non-parallel sides are of equal length. It is right angled if any one of the angles is 90 degrees.
The description given fits that of an isosceles trapezoid whereas non parallel sides are equal in length and base angles are equal in sizes.
I assume you mean 1 pair of parallel lines, which would describe a trapezoid.
A trapezoid is a polygon. Therefore, a trapezoid has no height
A trapezoid with congruent diagonals is an isosceles trapezoid.