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
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.
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°.