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Lesson 3 : (1.5 ) Measuring Segments (1.6) Measuring Angles

Lesson 3 : (1.5 ) Measuring Segments (1.6) Measuring Angles. “Keep in mind that the true measure of an individual is how he treats a person who can do him absolutely no good.” -Ann Landers. What are we learning?. Students will…

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Lesson 3 : (1.5 ) Measuring Segments (1.6) Measuring Angles

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  1. Lesson 3: (1.5)Measuring Segments (1.6) Measuring Angles “Keep in mind that the true measure of an individual is how he treats a person who can do him absolutely no good.” -Ann Landers

  2. What are we learning? • Students will… • find the measures of segments as well as angles using the segment addition and the angle addition postulates. Evidence Outcome: Students will express properties with equations (coordinate geometry). (HS 4.3a) Purpose (Relevancy): The highway can be seen as a number line. By applying the segment addition postulate, a person could find the distance from one exit to another.

  3. Postulate 1-5 The Ruler Postulate: 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 The distance between points A and B on the ruler is 7. To find the length of AB, find the absolute value of the difference of the coordinates of A and B, called “a” and “b.” AB = |a - b| A B

  4. Postulate 1-5 The Ruler Postulate: The distance between any two points is the absolute value of the difference of the corresponding numbers Example: Using AB = |a - b| Find: DE EG DG E G D -7 5 -2 0

  5. Congruence Congruent Segments: Segments that have the same length Example: Which of the following are congruent? How do we show congruence? If AB = CD, then AB ≅ CD AB ≅ CD = B 3 in. = C 4 in. A 3 in. E F D

  6. 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 XZ = 88, find the value of x. Then find the values of XY and YZ 3x - 2 4x + 6 X Y Z

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

  8. Postulate 1 - 8 Angle Addition:If point B is in the interior Of <AOC, then <AOB + <BOC = <AOC B A O C Example:If <POW is 97°and <POQ is 29o, what is <QOW Q P W O

  9. Lesson 3: (1.5) Measuring Segments (1.6) Measuring Angles HW: Pgs. 33-34; 6-14 e, 20-23, 35-37 Pgs. 40-41; 1-14 a “Keep in mind that the true measure of an individual is how he treats a person who can do him absolutely no good.” -Ann Landers

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