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DO NOW

DO NOW. Ruler Postulate. The distance between any two points on the number line is the absolute value of the difference of their positions. AB = |a – b| a = coordinate of point A b = coordinate of point B. B. E. A. C. D. -8. -6. 1. 3. 7.

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DO NOW

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  1. DO NOW

  2. Ruler Postulate The distance between any two points on the number line is the absolute value of the difference of their positions. AB = |a – b| a = coordinate of point A b = coordinate of point B

  3. B E A C D -8 -6 1 3 7 Find the length of the segments:1. AC = 2. BD = 3. AD = 4. BE = Solution: 1. AC = 9 2. BD = 9 3. AD = 11 4. BE = 13

  4. 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

  5. R S T Example 1: If RS = 15 and ST = 9, then RT = ? Example 2. If ST = 15 and RT = 40, then RS = ? Solution: 1. RT = RS + ST = 15 + 9 = 24 Solution: 2. RT = RS + ST 40 = RS + 15 RS = 25

  6. 2x - 8 3x - 12 D S T Example 3: If DT = 60, find the value of x. Then find DS and ST: Solution: DS + ST = DT (2x – 8) + (3x – 12) = 60 5x – 20 = 60 simplify 5x = 80 add 20 to each side x = 16 divide each side by 5 DS = (2x – 8) = 2 (16) – 8 = 24 ST = (3x – 12) = 3 (16) – 12 = 36

  7. Measuring Angles An angle is formed by two rays with the same endpoint. This common endpoint is called the vertex. Angle can be named as: ABC, CBA, B, 1. A B 1 C

  8. Measuring Angles Angles are measured in degrees. The measure of A is written as m A For example: m A = 80º. 80º A

  9. Angles classified by measure • Acute Angle: 0º < x < 90º • Right Angle: x = 90º • Obtuse Angle: 90º < x < 180º 4. Straight Angle: x = 180º

  10. How do we measure angles ?? Angles are measured using protractors.

  11. Using your protractors construct the angles measuring: • 35 º 2. 90 º 3. 105 º 4. 180 º

  12. A B O C Angle Addition Postulate If point B is in the interior of AOC, then m AOB + m BOC = m AOC

  13. T W R S G D F E Example 1: m RST = 50º and m RSW = 125º. What is m TSW? Example 2: m DEG = 145º. What is m GEF? Solution 1. 75º Solution 2. 35º

  14. Concepts of congruent segments Segments that have the same measure are congruent segments. Symbol of congruence AB CD D A 1.7 cm 1.7 cm C B

  15. HW Section 1.2, pg. 18-19, #5-8, 16-19, 21, 22, 27-29.

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