no
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There are more than two: A parallelogram has two sets of parallel line segments which may be of unequal length; A rectangle is a parallelogram that has line segments that meet at right angles; A rhombus has to sets of parallel line segments which are all of the same length; A square is a rhombus which has line segments meeting at right angles, or stated differently a square is a rectangle which has all line segments of the same length.
no They just have to have four sides the same length and the oppsite line segments must be parallel.
Lines in the same plane that are not parallel are intersecting lines.
No
A vertical line has an undefined slope. For the line to be parallel to a vertical line, the slopes would have to be the same. Therefore, the line parallel to a vertical line also has an undefined slope.