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Download 1-3 Measuring and Constructing Angles Angle
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1-3 Measuring and Constructing Angles Angle—formed by two rays with a common endpoint. The rays are the sides of the angle. Vertex—the common endpoint of the sides of the angle. B is the vertex of this angle. Interior of an angle—The set of all points between the sides of the angle Exterior of an angle—the set of all points outside the angle exterior Interior Different ways to name the above angle: < B, <ABC, <CBA, <1 Remember to put the vertex point in the middle when naming an angle with 3 letters. BA and BC are the sides of this angle. A B C D You cannot name an angle just by its vertex if there is more than one angle with the same vertex. In the above example, there would be three <B’s, so you must specify which <B. Measure of an angle—is given in degrees. Protractor Postulate—Given AB and a point O on AB , all rays that can be drawn from O can be put into a one-to-one correspondence with the real numbers from 0 to 180. Protractor—an instrument used to measure the degrees of an angle. The degrees of an angle range from 0 < x < 180°. To use, put the circle in the middle on top of the vertex of the angle and the line with extends from the small circle on one of the rays. Extend the other ray and see where it hits on the scale. Be careful: look to see if the angle is smaller or larger than a right angle. That will determine which number you will use for the degrees. If less than 90°, you will use the degrees less than 90. If greater than 90°, you will use the numbers greater than 90. Types of Angles Acute angle --Measures greater than 0° and less than 90°. Interval notation: 0 < x < 90 Right angle—measures exactly 90° x = 90 Obtuse angle—measures greater than 90° and less than 180° Interval notation 90< x < 180 Angle Addition Postulate If S is in the interior of <PQR, then the m<RQS + m<SQR = m<PQR. m stands for measure. Since we have equal signs, we are dealing with actual numbers. Angle Bisector -a ray or line that divides the angle into two congruent angles. Line segment BE bisects < ABC, therefore < ABE is congruent to < EBC m < ABE = m <EBC m < ABE = ½ m < ABC, m < EBC = ½ m < ABC ray bisecting an angle
