Question

The steps to use a compass and straightedge to construct a parallel line to a given line, l, that passes through a point not on that line, P, are given below. Arrange them in the correct order. Use a straightedge to draw a line through points P and Q. Mark the point of intersection between the two arcs as point Q. Use a straightedge to draw line m that intersects line l and point P. Adjust the compass so it is equal to the distance between the intersection points of the first arc and lines l and m. Draw the point of intersection between line l and line m. Without changing the compass width, construct an arc from point Z that intersects the previously constructed arc. Without changing the compass width, construct a second arc from point P that intersects line m at point Z. Using a compass, swing an arc that intersects lines l and m from the point of intersection.

Answer 1

The first step has to only use the givens, and each step can only use what comes before.

1. Use a straightedge to draw line m that intersects line l and point P.

2. Draw the point of intersection between line l and line m.

3. Using a compass, swing an arc that intersects lines l and m from the point of intersection.

4. Adjust the compass so it is equal to the distance between the intersection points of the first arc and lines l and m.

5. Without changing the compass width, construct a second arc from point P that intersects line m at point Z.

6. Without changing the compass width, construct an arc from point Z that intersects the previously constructed arc.

7. Mark the point of intersection between the two arcs as point Q.

8. Use a straightedge to draw a line through points P and Q.