# compass and straightedge construction of regular triangle

One can construct a regular triangle with sides of a given length $s$ using compass and straightedge as follows:

1. 1.

Draw a line segment  of length $s$. Label its endpoints $P$ and $Q$.

2. 2.

Draw an arc of the circle with center $P$ and radius $\overline{PQ}$.

3. 3.

Draw an arc of the circle with center $Q$ and radius $\overline{PQ}$ to find a point $R$ where it intersects the arc from the previous step.

4. 4.

Draw the regular triangle $\triangle PQR$.

This construction is justified by the following:

This construction also yields a method for constructing a $60^{\circ}$ angle using compass and straightedge.

Note that, with the exception of actually drawing the sides of the triangle  , only the compass was used in this construction. Since regular triangles tessellate, repeated use of this construction provides a way to find infinitely many points on a line given two points on a line using just a compass.

If you are interested in seeing the rules for compass and straightedge constructions, click on the provided.

Title compass and straightedge construction of regular triangle CompassAndStraightedgeConstructionOfRegularTriangle 2013-03-22 17:19:10 2013-03-22 17:19:10 Wkbj79 (1863) Wkbj79 (1863) 10 Wkbj79 (1863) Algorithm  msc 51M15 msc 51-00 compass and straightedge construction of equilateral triangle compass and straightedge construction of equiangular triangle compass and straightedge construction of $60^{\circ}$ angle