Geometry for Elementary School/Our tools: Ruler and compass

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Geometry for Elementary School
Construction Our Tools: Ruler and compasses Constructing equilateral triangle


This is a picture of a pair of compasses and a ruler.

How to draw a line[edit]

Using a ruler (based on Book I, Postulate 1), we can draw a segment of 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 segment \overline{AB}
Line segment \overline{BA}

How to draw a circle[edit]

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

Geom draw circle sequence.png

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.