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Measurement and Congruence of Segments and Angles

Learn about measuring segments and angles using rulers and protractors, and understand the concept of congruent segments. Practice solving problems involving segment addition, angle addition, and finding unknown lengths and measures.

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Measurement and Congruence of Segments and Angles

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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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