# Constructing a Segment

Start by assembling a checklist of techniques for constructing segments whose length is some multiple of $a$. For example, can you construct one with length $ka$ (where $k$ is a whole number)? What about $a/k$? ... or $\sqrt2a$? What about $\sqrt ka$ for other values of $k$? (Think of a right-angled triangle in which two sides are known multiples of $a$. What will be the length of the hypotenuse?)