Lesson 1.5: Measuring Segments Lesson 1.6a: Measuring Angles

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Presentation transcript:

Lesson 1.5: Measuring Segments Lesson 1.6a: Measuring Angles

Absolute Value A number’s distance from zero. REMEMBER: DISTANCE IS ALWAYS POSITIVE!

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 , is written as AB (no line above the letters!) Ex: 1. Find DE 2. Find CE 3. Find AC

Congruence If AB = BC, then Congruent Segments: Segments that have the same length If AB = BC, then Ex: Are and congruent? (Check if AB = BC) Do you see any other pairs of congruent segments?

Postulate 1-6 A Segment Addition Postulate: If 3 points A, B, and C are collinear and B is between A and C, then AB + BC = AC B C Example: If TV = 46, find the value of x. Then find the values of TU and UV. T U V 3x - 2 4x + 6

Postulate 1-6 A Segment Addition Postulate: If 3 points A, B, and C are collinear and B is between A and C, then AB + BC = AC B C Example: Q is the midpoint of . Find PQ, QR, and PR. P Q R 2x + 14 5x + 2

Angles Angle: An angle is formed by two rays with the same endpoint. B K 1 Name: Name: J C R P 2 3

Types of Angles Acute Angle: less than 90° Right Angle: Exactly 90° Straight Angle: exactly 180° Obtuse Angle: more than 90° 8

Postulate 1-7 Protractor Postulate: O is a point with opposite rays called and going to the left and right. Any ray drawn up from O creates and angle with a measure between and . Let’s talk about measuring angles with a protractor…

180

Postulate 1 - 8 Angle Addition Postulate: Angle Addition Postulate: Ex: Ex.

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