# compass and straightedge construction of square

One can construct a square 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.

Extend the line segment past $Q$.

3. 3.

Erect the perpendicular to $\overrightarrow{PQ}$ at $Q$.

4. 4.

Using the line drawn in the previous step, mark off a line segment of length $s$ such that one of its endpoints is $Q$. Label the other endpoint as $R$.

5. 5.

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

6. 6.

Draw an arc of the circle with center $R$ and radius $\overline{QR}$ to find the point $S$ where it intersects the arc from the previous step such that $S\neq Q$.

7. 7.

Draw the square $PQRS$.

This construction is justified because $PS=PQ=QR=QS$, yielding that $PQRS$ is a rhombus. Since $\angle PQR$ is a right angle, it follows that $PQRS$ is a square.

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

Title compass and straightedge construction of square CompassAndStraightedgeConstructionOfSquare 2013-03-22 17:19:13 2013-03-22 17:19:13 Wkbj79 (1863) Wkbj79 (1863) 5 Wkbj79 (1863) Algorithm msc 51M15 msc 51-00