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A trapezoid, although not all trapezoids will have two right angles. See the related link for a picture.
____________ / | /_____________ | Crappy drawing, I know, but a right trapezoid has two right angles(right side of picture), and two supplimentary non-right angles(left side of drawing). This is still a trapezoid because in order to be a trapezoid, there must be one and only one pair of parallel lines, and four sides. That's it, thus this is a possible trapezoid.
A trapezoid is a polygon. Therefore, a trapezoid has no height
A trapezoid with congruent diagonals is an isosceles trapezoid.
Well, think for a moment. (You can do it !) Try and picture a kite, a parallelogram, a trapezoid, and a rhombus. They're all quadrilaterals, but none of them is a rectangle.