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Geometry: Constructions



Angles, page 2

page 1 of 2

An angle is a geometric figure consisting of two rays with a common endpoint. It looks like this:

Figure %: Angle ABC
The common endpoint is called the vertex of the angle; in this case the vertex is point A, which is a part of the ray AB as well as the ray AC. The angle can be called either angle CAB or angle BAC. The only rule in naming an angle is that the vertex must always be the middle "initial" of the angle. The symbol for an angle is this:

Figure %: The symbol for angle ABC

Measuring Angles

Long ago people wanted to measure angles, so numbers were arbitrarily assigned to determine the size of angles. Under this arbitrary numbering system, one complete rotation around a point is equal to a 360 degree rotation. (There is another unit of measure for angles besides degrees called radians, in which one full rotation is equal to 2Π radians; in this text we will use degrees as our default unit for measuring angles.) Two angles with the same measure are called congruent angles. Congruence in angles is symbolized by a small arc drawn in the region between rays. Congruent angles are drawn with the same number of such arcs between their rays. An angle's measure determines how it is classified.

Zero Angles

An angle with a measure of zero degrees is called a zero angle. If this is hard to visualize, consider two rays that form some angle greater than zero degrees, like the rays in the . Then picture one of the rays rotating toward the other ray until they both lie in the same line. The angle they create has been shrunk from its original measure to zero degrees. The angle that is now formed has a measure of zero degrees.

Figure %: A zero angle

Right Angles

An angle with a measure of 90 degrees is called a right angle. A right angle is symbolized with a square drawn in the corner of the angle.

Figure %: A right angle

Straight Angles

An angle with a measure of 180 degrees is called a straight angle. It looks just like a line. Don't mix up straight angles with zero angles.

Figure %: A straight angle

Acute and Obtuse angles

Another way to classify angles by their measures is to consider whether the angle's measure is greater or less than 90 degrees. If an angle measures less than 90 degrees, it is called an acute angle. If it measures more than 90 degrees, it is called an obtuse angle. Right angles are neither acute nor obtuse. They're just right.

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