Cumulative Assessment
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We are essentially creating two congruent corresponding angles.
See solution.
In step 1, we draw a transversal to line m that also passes through point P.
The next step is to create two identical arcs, one around the point of intersection, Q, line m and the transversal and another around point P. This makes sure that we can copy the angle.
In the third step, we measure the angle between line m and the transversal using the first arc. We then copy this measurement on our second arc. This makes AB=CD and AP=BD. This means that the new line with be a constant distance from m, and will have the same slope.
Having marked point D in step 3 that copies the angle around point Q, we can draw a parallel line to line m.