MATH325: Lecture 11

Syllabus | Schedule | Grading Keys/Rubrics

Straightedge and Compass rules

The textbook gives 4 rules for straightedge and compass construction which clarify what can and can't be used. While Euclid's postulates are a helpful guideline for constructions, these are very clear and direct and worth taking as the rules used in our class.

  1. We start with two distinct points in the plane.
  2. We can draw a line through any two already constructed points.
  3. We can draw a circle with center an already constructed point, and through another already constructed point.
  4. We can construct points which are at the intersection of two distinct constructed lines, two distinct constructed circles, or a constructed line and a constructed circle.
Notice that at this point we don't even need to make assumptions about lines or circles interesecting. But if they do, we can construct those points of intersection!

More Constructions

Given two points O and Q, construct the midpoint of segment OQ.

Were you able to solve this after looking at Figure 3.1(b)? How many steps did you use to solve it? How do you know that the point you constructed is the midpoint?

If you had trouble with any of this, take a look at Lemma 3.3.2, which describes the construction of a the perpendicular bisector of a segment and also proves that the constructed line must be the perpendicular bisector. This would be a good proof to study for Test 2.

Review of Triangle Congruence Theorems