These constructions are mathematical games that produce figures, precisely drawn figures, which are accurately done without the aid of any measuring device. The student uses only a compass and a straightedge. These constructions require a certain level of skill with these instruments. Without such a skill the student’s drawing will be poorly done.
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.
Given: A line and a point on that line
Construct: A perpendicular line through that point
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.