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Definitions and Postulates Segments, Rays, and Distance

Definitions and Postulates Segments, Rays, and Distance. Chapter 1-3 p.11. Definitions/ Naming. Line Segments Endpoints Rays. Opposite Rays (hands on a clock at 6:00pm) Coordinate (on a number line)- number paired with a point. Distance. Length of a segment = distance between endpoints

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Definitions and Postulates Segments, Rays, and Distance

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  1. Definitions and PostulatesSegments, Rays, and Distance Chapter 1-3 p.11

  2. Definitions/ Naming • Line Segments • Endpoints • Rays

  3. Opposite Rays (hands on a clock at 6:00pm) • Coordinate (on a number line)- number paired with a point

  4. Distance • Length of a segment = distance between endpoints • Always positive • On a number line, • Distance=absolute value of the difference in coordinates of two points • Length of segment AB? AB = • Length of segment BC? BC = • Distance between point A and point C? AC ● ● ● __ __

  5. Ruler Postulate • Points on a line can be paired with real numbers in such a way that any two points can have coordinates 0 and 1. • Once a coordinate system has been chosen this way, the distance between any two points equals the absolute value of the difference of their coordinates. • Example: Engineer’s/Architect’s ruler

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

  7. More Definitions… • Congruent segments have equal length • AB = BC (lengths are equal) and • AB BC (segments are congruent) • Midpoint (of a segment)- point that divides the segment into two congruent segments • Bisector (of a segment)- line, segment, ray, or plane that intersects the segment at its midpoint ● ● ● l __ __

  8. Additional Thoughts… ___ • When P is the midpoint of AB, AP = PB • However, when SM = MT, M is not necessarily the midpoint of ST • When is M not the midpoint of ST? ___ ___ M S T

  9. Fill in the blank with always, sometimes, or never • The length of a segment is _______ negative. • If point S is between points R and V, then S _______ lies on RV. • A coordinate can _________ be paired with a point on a number line. • A bisector of a segment is ___________ a line. • A ray __________ has a midpoint. • Congruent segments ___________ have equal lengths. • AB and BA __________ denote the same ray. never always always sometimes never always never

  10. Homework • Classroom Exercises p.14 #1-14 and 23-26

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