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Unformatted text preview: Slide 9  1 Chapter 9 Geometry Slide 9  2 9.1 Points, Lines, Planes, and Angles Slide 9  3 Basic Terms A point , line , and plane are three basic terms in geometry that are NOT given a formal definition, yet we recognize them when we see them. A line is a set of points. Any two distinct points determine a unique line. Any point on a line separates the line into three parts: the point and two half lines. A ray is a half line including the endpoint. A line segment is part of a line between two points, including the endpoints. Slide 9  4 Basic Terms Line segment AB Ray BA Ray AB Line AB Symbol Diagram Description AB uur s AB uuur BA uuur AB A B A A A B B B Slide 9  5 Angles An angle is the union of two rays with a common endpoint; denoted The vertex is the point common to both rays. The sides are the rays that make the angle. There are several ways to name an angle: R . R R R , , ABC CBA B Slide 9  6 Angles The measure of an angle is the amount of rotation from its initial to its terminal side. Angles can be measured in degrees, radians, or , gradients. Angles are classified by their degree measurement. Right Angle is 90 ° Acute Angle is less than 90 ° Obtuse Angle is greater than 90 ° but less than 180 ° Straight Angle is 180 ° Slide 9  7 Angles Angles are classifies by their degree measurement. x = 90 o x < 90 o 90 o < x < 180 o x = 180 o x x x x RIGHT ANGLE ACUTE ANGLE STRAIGHT ANGLE OBTUSE ANGLE Slide 9  8 Types of Angles Adjacent Anglesangles that have a common vertex and a common side but no common interior points. Complementary Anglestwo angles whose sum of their measures is 90 degrees. Supplementary Anglestwo angles whose sum of their measures is 180 degrees. Slide 9  9 Example 1: Determining Complementary and Supplementary Angles a. ABC and CBE are supplementary angles. Determine m CBE b. ABC and CBD are complementary angles. Determine m CBD A B 55 o C R E D R R R R R Slide 9  10 a. ABC and CBE are supplementary angles. Determine m CBE The sum of supplementary angles = 180 o Therefore ABC + CBE = 180 o 55 o + CBE = 180 o CBE = 180 o – 55 o CBE = 125 o A B 55 o C E D R R R R R R R R Example 1: Determining Complementary and Supplementary Angles Slide 9  11 a. ABC and CBD are complementary angles. Determine m CBD The sum of complementary angles = 90 o Therefore ABC + CBD = 90 o 55 o + CBD = 90 o CBD = 90 o – 55 o CBD = 35 o A B 55 o C E D R R R R R R R R Example 1: Determining Complementary and Supplementary Angles Slide 9  12 Example 2 If are supplementary and the measure of ABC is 6 times larger than CBD, determine the measure of each angle....
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This note was uploaded on 12/12/2011 for the course MGF 1106 taught by Professor Holbrook during the Spring '10 term at Santa Fe College.
 Spring '10
 HOLBROOK

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