1.3 Segments, Rays, and Distance

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 A B

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 AB A B

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

5. Examples of Opposite Rays

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

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

8. Number Lines • On a number line every point is paired with a number and every number is paired with a point. K M J

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

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

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

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

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

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

19. A B C 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.

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

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

25. Remote time

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

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

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

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