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Understanding Line Segments: The Ruler Postulate and Congruent Segments

In this lesson, we explore essential concepts in geometry, focusing on measuring segments using the Ruler Postulate, which establishes a one-to-one correspondence between points on a line and real numbers, allowing us to determine distances. We define congruent segments and examine segment addition, midpoint, and segment bisectors. Through practical exercises, we apply these concepts to find lengths, evaluate congruency, and determine values of unknown variables in segment equations. Reinforce your understanding with practice problems centered around these foundational topics.

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Understanding Line Segments: The Ruler Postulate and Congruent Segments

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  1. Measuring Segments Geometry Mrs. King Unit 1, Lesson 4

  2. Ruler Postulate 1-5: The points of a line can be put into a 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.

  3. Practice Find QS (“the length of segment QS”) if the coordinate (“location”) of Q is –3 and the coordinate of S is 21.

  4. Definition Congruent: Two segments with the same length. () http://hotmath.com/hotmath_help/topics/congruent-segments/congruent-segments.gif

  5. Find which two of the segments XY, ZY, and ZW are congruent. Because XY = ZW, XYZW. Practice XY = | –5 – (–1)| = | –4| = 4 ZY = | 2 – (–1)| = |3| = 3 ZW = | 2 – 6| = |–4| = 4

  6. Segment Addition Postulate 1-6: If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. C B A

  7. If AB = 25, find the value of x. Then find AN and NB. Practice AN + NB = AB (2x – 6) + (x + 7) = 25 3x + 1 = 25 3x = 24 x = 8 AN = 2x – 6 = 2(8) – 6 = 10 NB = x + 7 = (8) + 7 = 15

  8. Practice 2x - 8 3x - 12 If DT = 60, find the value of x. Then find DS and ST. D S T

  9. Definition Midpoint: a point that divides the segment into two congruent segments Segment Bisector: a line, segment, ray, or plane that intersects a segment at its midpoint

  10. Practice Mis the midpoint of RT. Find RM, MT, and RT. RM = MT 5x + 9 = 8x – 36 +36+36 5x+ 45 = 8x -5x-5x 45 = 3x 15 = x RM = 5x + 9 = 5(15) + 9 = 84 MT = 8x – 36 = 8(15) – 36 = 84 RT = RM + MT = 168

  11. Homework Measuring Segments in Student Practice Packet (Page 5, #1-12)

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