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.
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.
|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)|