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Measuring Segments and Angles Finding Segment Lengths To find the distance between two points on a number line, there is a need to use the Ruler Postulate. Finding Segment Lengths Postulate 1-5 The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers. Finding Segment Lengths Postulate 1-5 AB a b coordinate length of A of AB coordinate of B Finding Segment Lengths Two segments with the same length are congruent ( ) segments. The statement that congruent segments are segments with the same length is also true. Finding Segment Lengths Postulate 1-6 Segment Addition Postulate If three points, A, B, and C are collinear and B is between A and C, then AB + BC = AC. Finding Segment Lengths http://www.phschool.com/atschool/academy1 23/english/academy123_content/wl-bookdemo/ph-355s.html Finding Segment Lengths A midpoint of a segment is a point that divides a segment into two congruent segments. A midpoint, or any line, ray, or other segment through a midpoint, is said to bisect the segment. Finding Segment Lengths http://www.phschool.com/atschool/academy1 23/english/academy123_content/wl-bookdemo/ph-356s.html Finding Angle Measures An angle is formed by two rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle. Finding Angle Measures One way to measure an angle is in degrees, To indicate the size or degree measure of an angle, write a lower case m in front of the angle symbol. Finding Angle Measures Postulate 1-7 : Protractor Postulate Let ray OA and ray OB be opposite rays in a plane. Rays OA, OB and all the rays with endpoint O can be drawn on one side of line AB can be paired with the real numbers from 0 to 180 so that ray OA is paired with 0 and ray OB is paired with 180. If ray OC is paired with x and ray OD is paired with y, then the measure of angle COD is x y Finding Angle Measures Wy WX Finding Angle Measures Angles can be classified according to their measurements: Acute angle : 0 < x < 90 Right angle: x = 90 Obtuse angle: 90 < x < 180 Straight angle: x = 180 Finding Angle Measures http://www.phschool.com/atschool/academy12 3/english/academy123_content/wl-bookdemo/ph-760s.html Finding Angle Measures Postulate 1-8 : Angle-Addition Postulate If point B is in the interior of angle AOC, then measure of angle AOB plus the measure of angle BOC is equal to the measure of angle AOC. Finding Angle Measures If angle AOC is a straight angle, then the measure of angle AOB plus the measure of angle BOC is equal to 180. Finding Angle Measures http://www.phschool.com/atschool/academy1 23/english/academy123_content/wl-bookdemo/ph-357s.html Finding Angle Measures Angles with the same measure are congruent angles. In the same manner, if two angles are congruent then their measures are equal.
