# Greek Civilization

## The Early Greeks Contribution to Geometry

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## GEOMETRIC CONSTRUCTIONS

With that caveat in mind, and with the presumption that each student doing the following has the necessary skills:

**
CONSTRUCTION # 1
**

Given: An angle

Construct: A bisector of that angle

Have students draw an angle on their paper. Any size angle will work, but an acute angle is best to tackle as a beginner. The teacher may want to pass out a copy of an angle so that everyone starts with the same size angle.

If the student places the pivot of the compass on the vertex of the angle, and then draws an arc which sweeps across the sides of the angle, he will have identified two points, one on each side where the arc intersects them.

Using these points, the student places the pivot of the compass on one at a time, drawing an arc in the interior of the angle.

The two arcs intersect in the interior producing one point. A line is then drawn from the vertex of the given angle through this new point.

This construction is finished.

**
CONSTRUCTION #2
**

Given: A line and a point on that line

Construct: A perpendicular line through that point

**
CONSTRUCTION #3
**

Given: A line and a point not on that line

Construct: A perpendicular line through that point.

To conserve space these constructions are not included here. Each of these and others may be found in any basic geometry book.