It is often necessary to draw one line parallel to another under the restriction that the parallel line must pass through a point exterior to the original line. This construction provides a ready and easily performed method for accomplishing this task; since the parallel line is dependent on points discovered through the intersection of arc, it is somewhat more accurate than the previous construction using tangent points.

Given a Right Line AB and a point (C) outside that line, construct a second line that is parallel to Line AB and passes through Point C.

Select any point (D) on Line AB and open the compass to a length equal to the distance between Point C and Point D.

Using Point D as center describe an arc of a circle with a radius equal to the distance between Points C and D that cuts through Line AB below Point C at Point E.

Using Point E as center, describe an arc of a circle with a radius equal to the distance between Points C and D, being careful to extend this arc a bit farther from Line AB than the distance between Line AB and Point C.

Using Point C as center describe an arc of a circle with a radius equal to the distance between Point C and Point E that cuts Line AB at Point E.

Keeping the compass open to a length equal to the distance between Points C and E and using Point D as center, describe an arc of a circle that cuts the arc above Point D at Point F.

Produce a right line that passes through Point F and Point C. This line should be parallel to Line AB.

~ An Instructive Animation Wherein the Foregoing Construction is Visually Explained ~