# Greek Civilization

## The Early Greeks Contribution to Geometry

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## THE PROTRACTOR

*degree of arc*. These degrees can be further divided into minutes and seconds; however, it is not appropriate for this grade level to measure an angle with such precision. An angle is measured by a device called a protractor, which measures what portion of a circle the angle is “opened” up to. The protractor is one half of a circle, 180 degrees. It can be read from 0 to 180 degrees from the left side, or the right side. Two scales are drawn on most protractors to make it easy to use.

Demonstrate to students how an angle is measured. Give them practice in measurement of angles. In my experience this is a difficult task, as it is usually the first time they have ever used a protractor. Their precision in measurement should improve with practice.

Demonstrate how one draws an angle of a given measurement using a protractor. This task also requires a lot of practice. A good way to start out is for the student to first locate where he wants the vertex of the angle to be, and take it from there.

Have students measure angles from objects around them, i.e., tables, numbers on a clock, the spaces between their spread out fingers, the angle formed by stretching out their thumb and forefinger.

Give students practice in classifying angles according to the definitions given above.

When two lines intersect they form four angles. Two pairs of angles can be identified as opposite angles, or
*
vertical angles
*
.

*(figure available in print form)*

Also, 1 and 3 are vertical angles.

If 2 is 160°, what is the measure of 1? Consider the protractor. How many degrees are there in a half-circle? 1 and 2 together form a 180° angle, a straight line. Do you see the logic in that? What are the measures of the other angles?

Give students practice with this type of angle. Have then pick out vertical angles.

A ray that divides an angle into two equal parts is called the
*
bisector
*
of that angle. There is exactly one bisector to any given angle.

Give students plenty of practice with identifying bisectors of various angles. Use protractors a lot.

Some good practice on much of the work so far can be had by having students to make a paper airplane as they usually do, but instead of flying it they would unfold it and notice the angles that are formed Practice can be given with this on many of the skills thus far: labeling points, naming angles, measuring angles, adding and subtracting angles, naming line segments.