Geometry construction using a compass and straightedge

This page shows how to construct (draw) a 45 degree angle with compass and straightedge or ruler. It works by constructing an
isoscelesright triangle,
which has
interior angles
of 45, 45 and 90 degrees. We use one of those 45 degree angles to get the result we need. See the proof below for more details.

This construction works by creating an
isoscelesright triangle,
which is a
45-45-90 triangle.
The image below is the final drawing above with the red items added.

In isosceles triangle APC, base angles CPA and CAP are congruent.
(See Isosceles Triangles).
The third angle ACP is 90° and the interior angles of a triangle always add to 180.
So both base angles CPA and CAP are 45°.

Click here for a printable worksheet containing two 45° angle exercises.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.