Constructing a 30°- 60°- 90° triangle
Geometry construction using a compass and straightedge

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 30-60-90 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 step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.


  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 30-60-90 triangle (1), (2), (3)

  - Q.E.D

Try it yourself

Click here for a printable worksheet containing 30-60-90 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.
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Other constructions pages on this site




Right triangles

Triangle Centers

Circles, Arcs and Ellipses


Non-Euclidean constructions