Yes
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...parallel to each other.
Parallel lines never intersect and remain equal distance from each other but perpendicular lines intersect at right angles
No but its diagonals are perpendicular to each other
Not always because the diagonals of a rectangle bisect each other but they are not perpendicular to each other.
Yes the 4 corners of a rectangle are perpendicular to each other and its opposite sides are parallel to each other.