perpendicular line segment (apex)
~APEX~ A parallel line through a point not on the line
~APEX~ A parallel line through a point not on the line
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Although he presented it differently, the modern version is as follows:given a straight line and a point which is not on that line, there is only one line which will pass through the point and which is parallel to the line.
Euclid's parallel postulate.
perpendicular line segment (apex)
perpendicular line segment (apex)
~APEX~ A parallel line through a point not on the line
~APEX~ A parallel line through a point not on the line
~APEX~ A parallel line through a point not on the line
You can construct a parallel to a line through a point not on the line. (perpendicular line segment)
perpendicular line segment (apex)
Assume there are no lines through a given point that is parallel to a given line or assume that there are many lines through a given point that are parallel to a given line. There exist a line l and a point P not on l such that either there is no line m parallel to l through P or there are two distinct lines m and n parallel to l through P.
You construct a line perpendicular to the original and then a line perpendicular to this second line.
You construct a line perpendicular to the original and then a line perpendicular to this second line.
Rays pass through one point. Parallel lines never meet.