Segments and Angles

1. B 7 The points on a line can be given coordinates as if they were on a number line. This helps find the distance between the points A B A 2 2 7 If the coordinates of point A and point B are “2” and “7” then the distance between points A and B is the absolute value of the difference of the coordinates. The length of AB a = coordinate of point A b = coordinate of point B AB = a - b QS = -3 – 21 = -24 = 24 Segments and Angles Ex: Find QS if the coordinate of Q is –3 and the coordinate of S is 21.

2. 2cm A B A B Two segments with the same length are congruent ( =) 2cm ~ C D C D Lengths are AB = CD Segments are Congruent AB = CD ~ Segment Addition Postulate If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC A B C Ex: If DT = 60, find the value of x. Then find DS and ST. 2x - 8 3x - 12 D S T DS = 2(16) – 8 = 24 ST = 3(16) – 12 = 36 DS + ST = DT Segment Addition Postulate (2x – 8) + (3x – 12) = 60 Substitution 5x – 20 = 60 Combine like terms 5x = 80 Addition Property x = 16 Division Property

3. O P W 1 A A 1 POW We classify angles according to their measure from 0 to 180 . o o x o x o x o x o Acute Right Obtuse Straight o o o o 0 < x < 90 x = 90 x = 180 o o 90 < x < 180 Angles An Angle is formed by two rays with the same endpoint (called the vertex).

4. B A • If point B is in the interior of AOC, then m AOB + m BOC = m AOC C O B - If AOC is a straight angle, then m AOB + m BOC = 180 o o Ex: m TOP = 50 and m TOY = 125 . What is m POY = ? o A O P C Y T O Angle Addition Postulate