
Constructing a 30° 60° 90° triangle
This page shows to construct (draw) a
30 60 90 degree triangle
with compass and straightedge or ruler. We are given a
line segment
to start, which will become the
hypotenuse
of a 306090 right triangle. It works by combining two other constructions: A
30 degree angle, and a
60 degree angle.
Because the
interior angles
of a triangle always add to 180 degrees, the third angle must be 90 degrees.
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

Argument 
Reason 
1 
Angle ∠CPQ has a measure of 30° 
Constructed using the procedure described in
Constructing a 30° angle. See that page for method and proof. 
2 
Angle ∠CQP has a measure of 60° 
Constructed using the procedure described in
Constructing a 60° angle. See that page for method and proof. 
3 
Angle ∠PCQ has a measure of 90° 
Interior angles of a triangle add to 180°. Other two are 30° and 60°
See Interior angles of a triangle. 
4 
PQC is a 306090 triangle 
(1), (2), (3) 
 Q.E.D
Try it yourself
Click here for a printable worksheet containing 306090 triangle 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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