Constructing a parallel through a point (rhombus method)
This page shows how to construct a line
to a given line through a given point with compass and straightedge or ruler. This construction works by creating a
Since we know that the opposite sides of a rhombus are parallel, then we have created the desired parallel line. This construction is easier than the traditional
angle copy method since it is done with just a single compass setting.
Printable step-by-step instructions
The above animation is available as a
printable step-by-step instruction sheet, which can be used for making handouts
or when a computer is not available.
This construction works by creating a rhombus. Since we know that the opposite sides of a rhombus are parallel, then
we have created the desired parallel lines.
The diagram below is the final drawing above with the green lines added.
||Line segments RJ, JE, ES, RS are congruent
||All drawn with the same compass width.
||RJES is a rhombus
||A rhombus is a quadrilateral with 4 congruent sides.
||Lines RS and JE are parallel
Opposite sides of a rhombus are always parallel.
See Definition of a Rhombus
Try it yourself
Click here for a printable parallel line construction worksheet containing two problems to try.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Thanks to Eric Reppun, Sacred Hearts Academy, Honolulu, Hawaii for contributing this construction.
Other constructions pages on this site
Circles, Arcs and Ellipses
(C) 2011 Copyright Math Open Reference. All rights reserved