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Lesson 1.5: Measuring Segments Lesson 1.6a: Measuring Angles Absolute Value A number’s distance from zero. REMEMBER: DISTANCE IS ALWAYS POSITIVE! 9 3 8 3 0 Postulate 1-5 The Ruler Postulate: The distance between points on a number line (or on a ruler) is the absolute value of their difference. Remember: Distance is always positive! Note: The distance between A and B, or the length of AB , is written as AB (no line above the letters!) Ex: 1. Find DE 2. Find CE 3. Find AC Congruence Congruent Segments: Segments that have the same length If AB = BC, then AB BC Ex: Are AB and BC congruent? (Check if AB = BC) Do you see any other pairs of congruent segments? Postulate 1-6 Segment Addition Postulate: If 3 points A, B, and C are collinear and B is between A and C, then AB + BC = AC A B C Example: If TV = 46, find the value of x. Then find the values of TU and UV. 3x - 2 T 4x + 6 U V Postulate 1-6 Segment Addition Postulate: If 3 points A, B, and C are collinear and B is between A and C, then AB + BC = AC A B C Example: Q is the midpoint of PR . Find PQ, QR, and PR. 2x + 14 P 5x + 2 Q R Angles Angle: An angle is formed by two rays with the same endpoint. T B Name: 1 K Name: C J 2 P 3 R Types of Angles Acute Angle: less than 90° Obtuse Angle: more than 90° Right Angle: Exactly 90° Straight Angle: exactly 180° Postulate 1-7 Protractor Postulate: O is a point with opposite rays called OA and OB going to the left and right. Any ray drawn up from O creates and angle with a measure between 0 and 180. Let’s talk about measuring angles with a protractor… 180 0 180 0 Postulate 1 - 8 Angle AngleAddition AdditionPostulate: Postulate: Ex: What is mTSW if mRST 40 and mRSW 115 ? Ex. If mDEG 130, find mGEF Lesson 1.5: Measuring Segments Lesson 1.6a: Measuring Angles HW: p.33 #6-14 even, 20-23, 35-37 p.40 #1-8, 13-14 THT: Can do #1-7, 9-10, 13-16 Terms: acute angle, obtuse angle, right angle, straight angle, congruence