Suppose we wish to construct a line segment containing point a and perpendicular to segment bc. to do so with the fewest compass measurements, we should first

A length is constructible if it can be obtained from a nite number of applications of a compass and straightedge. A constructible number is a constructible length or the negative of a constructible length. The demonstrations in this section, elsewhere in the text, and in class emphasize three part of the problem solving process for constructions: 1. Investigation or analysis. The usual approach is to imagine the problem is solved and search for relationships or properties that will allow us to accomplish the construction. 2. Construction. We propose the steps in the construction and perform the construction. 3. Proof: We justify that the constructions steps are valid and that the construction accomplishes what it was supposed to do.