### 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.

- We start with two distinct points in the plane.
- We can draw a line through any two already constructed points.
- We can draw a circle with center an already constructed point,
and through another already constructed point.
- 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