Compass and Straight Edge Help
Introduction to Compasss and Straight Edge Instruments
In geometry, a construction is a drawing made with the simplest possible instruments. Constructions are a powerful learning technique, because they force you to think about the properties of geometric objects, independent of numeric lengths and angle measures. Constructions are also challenging intellectual games.
The most common type of geometric construction is done with two instruments, both of which you can purchase at any office supply store. One instrument lets you draw circles, and the other lets you draw straight line segments. Once you have these, you can use them only according to certain “rules of the game.”
The draftsman's compass is a device for drawing circles of various sizes. It has two straight shafts joined at one end with a hinge. One shaft ends in a sharp point that does not mark anything, but that can be stuck into a piece of paper as an anchor. The other shaft has brackets in which a pen or pencil is mounted. To draw a circle, press the sharp point down on a piece of paper (with some cardboard underneath to protect the table or desk top), open the hinge to get the desired radius, and draw the circle by rotating the whole assembly at least once around. You can draw arcs by rotating the compass only partway around.
For geometric constructions, the compass must not have an angle measurement scale at its hinge. If it has a scale that indicates angle measures or otherwise quantifies the extent to which it is opened, you must ignore that scale.
A straight edge is any object that helps you to draw line segments by placing a pen or pencil against the object and running it alongside. A conventional ruler will work for this purpose, but is not the best tool to use because it has a calibrated scale. A better tool is a drafting triangle . Use any edge of the triangle as the straight edge.
Ignore the angles at the apexes of a drafting triangle. Some drafting triangles have two 45° angles and one 90° angle; others have one 30° angle, one 60° angle, and one 90° angle. You aren't allowed to take advantage of these standard angle measures when performing geometric constructions, so it doesn't matter which type of drafting triangle you use.
What's Allowed and Not Allowed When Using a Compass or Straight Edge
With a compass, you can draw circles or arcs having any radius you want. The center point can be randomly chosen, or you can place the sharp tip of the compass down on a predetermined, existing point and make it the center point of the circle or arc.
You can set a compass to replicate the distance between any two defined points, by setting the non-marking tip down on one point and the marking tip down on the other point, and then holding the compass setting constant.
With the straight edge, you can draw line segments of any length, up to the entire length of the tool. You can draw a random line segment, or choose a specific point through which the line segment passes, or connect any two specific points with a line segment.
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