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Understanding the Ruler Postulate and Segment Measurement in Geometry

This educational resource covers essential concepts in measuring segments using the Ruler Postulate. It explains how to assign real numbers (coordinates) to points on a line, allowing for the calculation of distances. The text details segment addition, congruence of segment lengths, and the definition of midpoints. Learners will discover how to apply the Segment Addition Postulate, determine congruent segments, and utilize midpoints effectively to solve geometry problems. This guide serves as a foundational tool for understanding geometric measurements.

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Understanding the Ruler Postulate and Segment Measurement in Geometry

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Presentation Transcript

  1. 1-3: Measuring Segments

  2. Ruler Postulate Ruler Postulate: Every point on a line can be paired with a real number. The real number that corresponds to a point is called the coordinate of the point.

  3. Distance • The Ruler Postulate allows you to measure lengths of segments using a given unit and to find distances between points on a number line. • The distancebetween points A and B is the absolute value of the difference of their coordinates. AB = |a – b| *Note: AB represents the length of AB.

  4. Measuring Segment Lengths • What is ST? • What is UV? • What is SV?

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

  6. Using the Segment Addition Postulate • If EG = 59, what are EF and FG?

  7. Congruence • When numerical expressions have the same value, you say that they are equal (=). • Similarly, if two segments have the same length, then the segments are congruent () *Note: Segments are can be marked to show congruence.

  8. Comparing Segment Lengths • Are AC and BD congruent? • Is AB congruent to DE?

  9. Midpoints • The midpoint of a segment is a point that divides the segment into two congruent segments. • A point, line, ray, etc. that intersects a segment at its midpoint is said to bisectthe segment and is called a segment bisector.

  10. Using the Midpoint • If Q is the midpoint, what are PQ, QR, and PR?

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