

Constructing a 45° angle
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
isosceles
right 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.
Printable stepbystep instructions
The above animation is available as a
printable stepbystep instruction sheet, which can be used for making handouts
or when a computer is not available.
Proof
This construction works by creating an
isosceles
right triangle,
which is a
454590 triangle.
The image below is the final drawing above with the red items added.
 Q.E.D
Try it yourself
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.
Other constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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