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Chapter 4 Geometry: Lines & Angles Point A location in space Line a straight path of points that goes on endlessly in both directions Line Segment a part of a line having two endpoints Plane a flat surface that goes on endlessly in all directions Ordered Pairs are two numbers that locate a point on a coordinate graph. The first is the X-axis (horizontal) the second, is the Y-axis (vertical) Coordinate Plane coordinate planes have four quadrants that show positive and negative axis Rays & Angles A RAY is a part of a line that goes on endlessly in one direction An ANGLE is formed when 2 rays share the same endpoint. The shared endpoint is called a VERTEX! Naming Angles * To name an angle, the vertex can be used alone, OR you can use the three points with the vertex in the middle. * The angles above can be called <A, <CAB, <BAC and <D, <EDF, <FDE Types of Angles Acute: cutie, less than 90 degrees Right: straight and strong, exactly 90 degrees Obtuse: big papa, greater than 90 degrees Straight: stretches out, exactly straight at 180 degrees Reflex: flexible angle, overextends more than 180 degrees Full Rotation: twirl, exactly 360 degrees Protractor * You use a protractor to measure angles. The VERTEX lines up with the center point on the bottom. The bottom ray lines up with the bottom of the compass line. The extending ray, tells you the measure of the angle in degrees. READ THE BOTTOM NUMBER if the angle is facing right, READ THE TOP NUMBER if the angle is facing left! Straight Angles Remember that Straight Angles ALWAYS equal 180 degrees. So if you know one angle, you can subtract it from 180 degrees to figure out the size of the other angle. Look at the example below. <AXC + <BXC = 180 62 + n = 180 180 - 62 = 118 So, <AXC = 118 degrees Measuring Angles Using a protractor, measure angles, remembering that angles facing right, use the bottom set of numbers. If the the angle is facing left, use the top set of numbers. Parallel Lines lines that run beside one another and will never cross Perpendicular Lines lines that intersect at exact right angles Intersecting Lines lines that will cross one another at various angle measurements Triangles A triangle can be classified by the measure of its angles. The sum of the measures of the angles of any triangle equals 180 degrees. Acute Triangle a triangle whose angles are all less than 90 degrees Right Triangle a triangle with one angle that is exactly 90 degrees Obtuse Triangle a triangle that has one angle that is over 90 degrees Remember!!!! ALL angles of a triangle (when added together) equal 180 degrees. EVERY TIME! No matter what kind of a triangle, or no matter what the size of the angles … the sum of the three angles together WILL BE 180 degrees guaranteed! Circles Radius a line segment from the center point to any point on the circle, a radius is 1/2 of a diameter, and is labeled as a line segment Chord a line segment that connects any two points on a circle, it is labeled like a segment Diameter a chord that passes through the center point, cutting the circle in half (180 degrees), it too is labeled as a segment Central Angle an angle with its vertex in the center of the circle, labeled like a normal angle Measuring Angles in a Circle You can measure a lot of angles in a circle simply by remembering a few things! 1. a diameter = straight angle = 180 degrees 2. right angles are 90 degrees 3. 1/2 of right angles are 45 degrees 4. the whole circle is 360 degrees 5. you can use subtraction to find the difference of the angles that are left