The Perpendicular Bisector construction is one that you will use over and over once you add it to your tool kit.  On it’s own, it will allow you to establish a working center line from a baseline.  Which is one of the most common starting points when beginning a design or layout.  Beyond that, the perpendicular bisector is the basis for numerous other geometric constructions.

The Perpendicular from a Point on a Line is another useful construction to establish a perpendicular to a baseline.  In this construction you will already have a point established on the baseline from which you want to then establish a perpendicular.  For design and layout work this is useful when you want to start laying out an object from an outside edge and work across it’s width.

The Perpendicular from a Point Above the Line is another method of establishing a perpendicular to an existing baseline.  In this instance the point will not be located on your baseline and you will drop a line from this point that intersects with the baseline at 90 degrees.  This construction utilizes the Perpendicular Bisector construction so it should be quite easy to learn and commit to memory.

Instructional Drawings:

perpendicular_bisector

perpendicular_point_on_line

perpendicular_point_above_line

Greg Merritt

Jim Tolpin, one of the authors of the book “By Hand &Eye” has posted animated clips of geometric constructions on his YouTube channel.

There is also information and animations on the Math Open Reference website.