1. 1.3 Segments, Rays, and Distance

2. Segment – Is the part of a line consisting of two endpoints & all the points between them. –Notation: 2 capital letters with a line over them. –Ex: –No arrows on the end of a line. –Reads: Line segment (or segment) AB AB AB

3. Ray – Is the part of a line consisting of one endpoint & all the points of the line on one side of the endpoint. –Notation: 2 capital letters with a line with an arrow on one end of it. End point always comes first. –Ex: –Reads: Ray AB A B AB

4. Opposite Rays – Are two collinear rays with the same endpoint. –Opposite rays always form a line. –Ex: Same Line QR S RQ & RS Endpoints

5. Examples of Opposite Rays

6. Ex.1: Naming segments and rays. Name 3 segments: –LP –PQ –LQ Name 4 rays: –LQ –QL –PL –LP –PQ LPQ Are LP and PL opposite rays?? No, not the same endpoints

7. Group Work Name the following line. Name a segment. Name a ray. X Y Z XY or YZ or ZX XY or YZ or XZ XY or YZ or ZX or YX

8. Number Lines On a number line every point is paired with a number and every number is paired with a point. JKM

9. Number Lines In the diagram, point J is paired with 8 We say 8 is the coordinate of point J. JKM

10. Length of MJ The length MJ, is written MJ It is the distance between point M and point J. JKM

11. Length of MJ You can find the length of a segment by subtracting the coordinates of its endpoints JKM MJ = 8 – 5 = 3 MJ = 5 - 8 = - 3 Either way as long as you take the absolute value of the answer.

12. Postulates and Axioms Statements that are accepted without proof Memorize all of them –Unless it has a name –Not “Postulate 6”

13. Ruler Postulate The points on a line can be matched, one- to-one, with the set of real numbers. The real number that corresponds to a point is the coordinate of the point. The distance, AB, between two points, A and B, on a line is equal to the absolute value of the difference between the coordinates of A and B.

14. Remote time

15. A- Sometimes B – Always C - Never The length of a segment is ___________ negative.

16. If point S is between points R and V, then S ____________ lies on RV. A- Sometimes B – Always C - Never

17. A coordinate can _____________ be paired with a point on a number line. A- Sometimes B – Always C - Never

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

19. Example 1 If B is between A and C, with AB = x, BC=x+6 and AC =24. Find (a) the value of x and (b) the length of BC. A C B

20. Congruent In Geometry, two objects that have –The same size and –The same shape are called congruent.

21. Congruent __________ Segments Angles Triangles Circles Arcs

22. Congruent Segments Have equal lengths To say that DE and FG have equal lengths DE = FG To say that DE and FG are congruent DE  FG 2 ways to say the exact same thing

23. Midpoint of a segment The point that divides the segment into two congruent segments. A B P 3 3

24. Bisector of a segment A line, segment, ray or plane that intersects the segment at its midpoint. A B P 3 3

25. Remote time

26. A bisector of a segment is ____________ a line. A- Sometimes B – Always C - Never

27. A ray _______ has a midpoint. A- Sometimes B – Always C - Never

28. Congruent segments ________ have equal lengths. A- Sometimes B – Always C - Never

29. AB and BA _______ denote the same ray. A- Sometimes B – Always C - Never