Geometry for elementary school/Our tools: Ruler and compass

Introduction

This is a picture of a compass and a ruler:

How to draw a line?

• Using the ruler (based on Book I, Postulate 1)

We can draw a straight line:

We will use the notation $\overline{AB}$ for the line segment the starts at A and ends at B. Note that we don't care about the segment direction and therefore $\overline{AB}$ is the same as $\overline{BA}$.

Line $\overline{AB}$:

Line $\overline{BA}$:

How to draw a circle?

• Using the compass (based on Book I, Postulate 3).

We use the notation $\circ A,\overline{AB}$ for the circle whose center is the point A and its radius length equals that of the segment $\overline{AB}$.

Note that in other sources, such as Euclid's Elements, a circle is described by any 3 points on its circumference, ABC.

The center-radius notation was chosen because of its suitability for constructing circles with a ruler and a compass.