Constructing Parallel Lines

How to construct parallel lines using a straight edge and a compass

Step 1:

Draw a line with you straight edge and put one point on the line and label it 1. Then put one point off the line and label it 2.

Step 2:

Connect point 1 and 2 with a straight edge.

Step 3:

Draw an arch at point 1.

Step 4:

Copy that arch at point 2.

Step 5:

Measure the arch at point 1 with your compass.

Step 6:

Then make an arch the distance of point 1's arch at point 2.

Step 7:

Finally, draw a line with your straight edge through point 2 and where the two archs intersect.

Comments

[grayl]

Among other things, that's what two triangles are for - drawing parallel lines.

[DavidF15]

Yes: you set one edge of a triangle along your first line, then set a straight edge along an adjacent side, then slide/translate the triangle along the straight edge until the initial edge of the triangle is at the point where you want the line, and then draw the new parallel line. It works by the principle of similar triangles.

[peabody1929]

This technique requires transferring a measurement. The lines will be only as parallel as the accuracy of the measurement. However, since we can construct a perpendicular line that does not require a measurement, we can construct a parallel line by constructing a perpendicular line to a perpendicular line. The net result is two lines that are parallel by construction. Using two triangles is the same idea--the two lines are parallel by definition.

[rafununu]

This is exactly what I thought !

[gilbequick]

Nice!

[Biblical scientist]

Its geometry, my dear Watson.

[seamster]

Nicely presented! :)