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.

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 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.

Constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Tangents

Ellipses

Polygons

Non-Euclidean constructions

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