A right angle triangle
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A polygon with four or more sides can meet all of the requirements.
The only requirement for a trapezoid is that one pair of opposite sides be parallel. There could be trapezoids with a pair of perpendicular lines.
Draw a line. Draw a perpendicular to that line then a perpendicular from that one.
since one parallel lines is perpendicular to another line, the other parallel line is perpendicular to the line as well. so the two would not be parallel, only the original two.
Only by coincidence. Two lines on a graph are perpendicular if and only if one slope is the negative reciprocal of the other: meaning that if one line has a slope of 3/2, the other would have to have a gradient of -2/3.