# Constructions

.

### Skip this boring introduction!

This page is dedicated to teaching you how to make constructions. This page would have been easier to understand if I was able to include our animation Java applet. Unfortunately, Dave never had a chance to complete this (even with the later deadline and working for 24 hours straight at a time). Kind of makes me glad I don't know Java. So, that'll have to wait until next year. Of course, this page would still be the same for those of you who can't read Java yet (i.e., most of us).

A construction is a specialized type of drawing. It is used to draw mathematical figures that require exactness. In a drawing you can use any tool. However, in a construction, you can only use two tools. They are the unmarked straightedge and the compass.

The straightedge is simply a flat tool with a straight edge or two. It is unmarked because specific lengths aren't used in a construction. That is, figures are of unspecified size in constructions - just bigger or smaller.

A compass is a tool used to draw circles. They are NOT the kind used to determine north or south. Compasses used for construction are tools that have one end with a sharp point and one end with a pencil or pen attached. It's sort of like two pens or pencils attached to each other at the erasers. A good compass is marked to determine the radius of the circle drawn, but that isn't necessary for a construction (as I've noted several times above). Anyways, you place the sharp point on the spot that you want to be the center of the circle, open the compass to the correct radius, and then move the pencil end in a circle. If you don't have one, it is easy to make one from scratch. Just tie a piece of string to the end of a pencil.

In a construction, three rules apply.

1. A point must either be given, or the intersection of previously constructed figures.
2. If a figure is given, you can assume as many points as necessary to make that figure.
3. A straightedge can draw the line through two points A and B, while a compass can draw a circle with center point A and containing a second point B.

.

## Circles

Do I even need to answer this one? If you want the answer that bad see the introductory paragraph on compasses or -gasp- the three rules to constructions.

.

## Perpendicular lines

Okay, this one's a legitimate question.

Please pardon the fact that the drawings may be a little inexact. It's a little hard to do with Paint Shop Pro.

1. First of all, you have to have a segment and a point in the line that is to be perpendicular, as you can see in the drawing.

2. Then you draw half of a circle at any radius so that the segment is intersected in two points. You can extend the segment a little if you have to.

3. Then you draw circles with each of the new points as centers and the distance between them as the radii.

4. The last step is to use the straightedge to connect the dots with the point A and the new points made by the intersections of the circles.

.

## Perpendicular bisectors

1. Just repeat steps 3-4 above, using the endpoints of the segment as the points in question. Connect the new points with each other to get the perpendicular bisector.

.

## Midpoints

1. Just find the perpendicular bisector of the segment. Its midpoint is the point of intersection of the two lines.

.

- Jaime III
"Art is a lie that makes us realize the truth." - Picasso