Their slopes are equal.
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4sides
their slopes are negative reciprocals.
Use two line segments (line A and line B) with all points on line A equidistant from all points on line B; in otherwords, use 2 parallel lines. Choose two points on line A (points a and b). Now choose 2 points on line B (x and y) so that the distance of line ab equals the distance of line xy. Connect points a and y with a line segment ab and points b and z with a line segment bz. In simpler words, take two parallel line segments of equal length, and connect their endpoints with two other line segments.
There are three lines in the figure described. Two of the lines never meet, these are the parallel lines. The third line crosses the other lines, it is the "transversal" line. If the parallel lines are really line SEGMENTS then each can be bisected (cut into two equal lengths) This is what your description states.
lines