Given a point $A$ on the line $m,$ it is possible to use a compass and straightedge to create a line that is perpendicular to $m$ and that passes through $A.$ This will be the unique line described by the Perpendicular Postulate.

First, place the sharp end of the compass at point $A,$ and draw a circle.

The circle intersects $m$ at two distinct points. These points will be named $X$ and $Y,$ for later referencing.

Place the sharp end of the compass at $X$ and draw an arc above point $A.$

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