Question

(PLEASE HELP) What are the steps for using only a compass and a straightedge to construct a line that is parallel to line PQ and passes through a point R that is not on PQ?

Answer 1

see attached for the construction

Explanation:

You want the steps for constructing a parallel line through a point not on the line.

Approach

There are a couple of different approaches that can be used:

1. copy an angle
2. construct perpendicular lines

The "copy an angle" method takes fewer steps.

Steps

1. Draw a line through R that crosses PQ at point J.
2. Draw an arc centered at J that crosses both lines.
3. Using the same radius, draw a similar arc centered at R.
4. Set the compass to the distance between the points where the arc centered at J crosses the two lines.
5. Using the same radius mark the same distance from line JR on the arc centered at R. Call that intersection of arcs point S.
6. Draw line RS parallel to PQ.

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Additional comment

The "perpendiculars" method constructs a perpendicular to PQ through point R, intersecting PQ at J. Then a perpendicular to RJ is constructed through point R.