The Parallel Postulate states that there exists exactly one line through a point, $P,$ that is parallel to a line, $l.$ This line can be found using a compass and a straightedge.

First, draw a line that intersects $l$ and goes through the point. The point where the new line intersects $l$ will be named $Q.$

Next, fix the sharp end of the compass at $Q$ and drawn an arc on $\overleftrightarrow{QP}$ between $Q$ and $P.$ With the same setting, draw an arc from $P$ across $\overleftrightarrow{QP}.$

Adjust the compass so that both ends align with the points where the first arc intersects both lines.

Using the setting above, place the sharp end of the compass where the second arc intersects $\overleftrightarrow{QP}.$ Draw an arc intersecting the second arc. The point where these arcs intersect can be named $R.$

Draw the line that connects points $P$ and $R.$

This line is parallel to $l.$

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