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Segments and Their Measures

This section covers fundamental concepts in geometry, including definitions of postulates, axioms, and theorems. It explores congruent segments, the Ruler Postulate, and the Segment Addition Postulate, explaining how to determine distances between points and establish relationships between segment lengths. The Distance Formula and the Pythagorean Theorem are introduced as tools for calculating distances in a coordinate plane. Example problems illustrate how to apply these concepts to find the length of segments in geometric contexts.

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Segments and Their Measures

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  1. Segments and Their Measures Section 1.3

  2. Definitions • Postulates- rules that are accepted without proof. • Axioms- same as Postulates • Theorems- rules that are proved. • Congruent Segments- segments that have the same length.

  3. Postulate 1: The Ruler Postulate • The distance between two points is the absolute value of the difference between the coordinates.

  4. Postulate 2Segment Addition Postulate • If B is between A and C, then AB + BC = AC. • If AB + BC = AC, then B is between A and C.

  5. Distance Formula • If A and B are points in a coordinate plane, then the distance between A and B is:

  6. Pythagorean Theorem • Can be used instead of the Distance Formula. a² + b² = c²

  7. Good Example • What is the length of AB if A(-1,1) and B(3,2)?

  8. Using Pythagorean Theorem • What is the length of AB if A(-1,1) and B(3,2)?

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