The Use of Compasses & Protractors in Math

Protractors are used for drawing and measuring angles.

In mathematics, compasses and protractors are used to draw and measure angles. Compasses are used to draw circles, while protractors measure angles of triangles. According to Independent Initiatives for Math and Science Education (IIMSE), students in California must know how to use these tools to meet state mathematical standards.

What are Compasses?

A compass is used to draw circles.

A compass is a tool used for drawing circles. The student places a sharpened pencil into one end of the compass and opens the compass to the desired radius. She draws a circle by rotating the end of the compass containing the pencil. According to the article "Geometric Construction With the Compass Alone", compasses are also used to find the intersection point between two circles, between a circle and a straight line, or between two straight lines.

What are Protractors?

Protractors typically have two measurements listed for each angle.

Protractors can be used to find the angles between two sides of a triangle or rectangle. The protractor consists of a straight edge and curved top. Most protractors have two sets of numbers marked on them; one for angles greater than 90 degrees, and one for angles less than 90 degrees. According to Math is Fun, students must judge whether an angle is greater or smaller than 90 degrees to determine which measurement to use for a given angle.

Comparison of Compasses and Protractors

Protractors and compasses are examples of geometric tools

Compasses and protractors both can be used to either draw or measure. Compasses can be used to measure the angle of intersection between lines, but it is far easier to use a protractor, as compass measurements are based on the measurements of arcs rather than lines.

Protractor Math Problems

Students can measure the angles in each shape to determine how many squares are in this picture.

Protractor problems typically ask the student to measure the angles of parallelograms or triangles. For example, students may be asked to measure all three angles of a triangle. The student can check his work by adding all three of the angles measured; if the sum is not 180 degrees, she has made a measurement error on one or more of the angles. Students may also be asked to determine whether a shape is a square by measuring the angles.

Compass Problems

A compass could be used to draw these intersecting circles in proportion.

Problems involving compasses are often involved. Students may simply be asked to draw a circle of a particular radius; however, compasses can also be used in more advanced classes to prove that two points lay on the same line or to use arcs to make lines of particular lengths.

References

• Cut the Knot: Geometric Construction With the Compass
• IIMSE: Math Connection - Lesson 1: The Protractor
• Math is Fun: Using a Protractor