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1.5 Segments & Their Measures

Learn about segments, their measures, and how to calculate distances between points. Explore concepts like collinear points, segment addition postulate, and congruent segments.

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1.5 Segments & Their Measures

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  1. 1.5 Segments & Their Measures

  2. B A x2 x1 Coordinate • The real number that corresponds to a point. • A & B are names for the points. • x1 and x2 are coordinates for the points.

  3. Distance A B • The length of AB can be found by x2-x1 • The symbol for the length of AB is AB. x1 x2

  4. Example 1: Find AB. A B Point A is at 1.5 and B is at 5. So, AB = 5 - 1.5 = 3.5

  5. C B A Between • When 3 points are on a line, one of them is between the other two. • B is between A & C.

  6. Example 1: Is Alex between Ty and Josh? Yes! In order for a point to be between 2 others, all 3 points MUST BE collinear (on the same line)!! Ty Alex Josh No, but why not? How about now?

  7. Measure (of a line segment) • The measure of a segment is the distance between the two endpoints. It is written as AB (with no segment over the letters.)

  8. Postulate • A statement that is accepted true without a proof.

  9. C B A Postulate 5: Segment Addition Postulate • If B is between A & C, then AB + BC = AC. • If AB + BC = AC, then B is between A & C.

  10. Example 3: if DE=2, EF=5, and DE=FG, find FG, DF, DG, & EG. D E F G FG=2 DF=7 DG=9 EG=7

  11. Congruent ( ) Segments • Segments that have the same length. If AB & XY have the same length, Then AB=XY, but AB XY Symbol for congruent

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