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Constructing a 30-60-90 triangle

This is the step-by-step, printable version. If you PRINT this page, any ads will not be printed.

See also the animated version.

After doing this Your work should look like this

We start with a line segment PQ that will be the hypotenuse of the triangle..

Geometry construction with compass and straightedge or ruler or ruler
First, we construct a 30° angle on one end of the hypotenuse. See Constructing a 30° angle.
1.  Starting with the hypotenuse line PQ, set the compasses on P, and set its width to any convenient width. Geometry construction with compass and straightedge or ruler or ruler
2.  Draw a broad arc across PQ. Label the point where it crosses PQ as point S. Geometry construction with compass and straightedge or ruler or ruler
3.  Without changing the compasses' width, move the compasses to the point S. Draw a broad arc that crosses the first one. Label the point where the two arcs cross as point T. Geometry construction with compass and straightedge or ruler or ruler
4.  Again without changing the compasses' width, move the compasses to the point T, and draw an arc across the previous arc, creating point R. Geometry construction with compass and straightedge or ruler or ruler
5.  Draw a line from P through R and continue it on beyond R to create the second side of the triangle. Geometry construction with compass and straightedge or ruler or ruler
Next, we construct a 60° angle on the other end of the hypotenuse. See Constructing a 60° angle.
6.  Place the compasses on point Q and set it to any convenient width. Geometry construction with compass and straightedge or ruler or ruler
7.  Draw a broad arc across PQ on the same side as point R. Label the point where it crosses PQ as point A. Geometry construction with compass and straightedge or ruler or ruler
8.  With the compasses on A, draw a second arc, crossing the first arc at point B Geometry construction with compass and straightedge or ruler or ruler
9.  Draw a line from Q, through B and on to cross the line PR. Label the intersection point C. Geometry construction with compass and straightedge or ruler or ruler
10.  Done. The triangle PQC is a 30-60-90 triangle. Geometry construction with compass and straightedge or ruler or ruler
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Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions