Editing Parallel (geometry) (section)

==== Construction ====
The three properties above lead to three different methods of construction<ref>Only the third is a straightedge and compass construction, the first two are infinitary processes (they require an "infinite number of steps".)</ref> of parallel lines.
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[[Image:Par-prob.png|thumb|left|250px|The problem: Draw a line through ''a'' parallel to ''l''.]]
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<gallery widths="200px">
image:Par-equi.png|Property 1: Line ''m'' has everywhere the same distance to line ''l''.
image:Par-para.png|Property 2: Take a random line through ''a'' that intersects ''l'' in ''x''. Move point ''x'' to infinity.
image:Par-perp.png|Property 3: Both ''l'' and ''m'' share a transversal line through ''a'' that intersect them at 90°.
</gallery>