You pass another line through both of them and measure the angles. If the first two lines form the same angle with the third line, the first two are parallel.
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No.
If the lines are straight and have the same slope they are parallel, no matter what the y intercept is
If the two lines are parallel, they will never connect. A straight line drawn across those lines will intersect them at identical angles. If you have perpendicular lines, they intersect and all four angles that they make are 90 degrees.
A trapezoid has two parallel lines.
They are parallel to each other.