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Segments and Their Measures

Explore definitions, postulates, and theorems related to congruent segments, distance formulas, and the Pythagorean theorem in geometry. Learn how to apply these concepts to solve problems effectively.

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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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