1 / 30

1.3 Segments, Rays, and Distance

1.3 Segments, Rays, and Distance. 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.

agnes
Download Presentation

1.3 Segments, Rays, and Distance

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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. Endpoint always comes first. • Ex: • Reads: Ray AB • The ray continues on past B indefinitely AB A B B A

  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 I want a real number as the answer • When I write MJ = “The length 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 • They are true and always will be true • They are used in helping to prove further Geometry problems, theorems….. • Memorize all of them • Unless it has a name (i.e. “Ruler Postulate”) • Not “Postulate 6” • named different in every text book

  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. (matching points up with a ruler) • 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. (absolute value on a number line)

  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 • Student demonstration • 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. (pg. 13) Write out the problem based on the segments, then substitute in the info

  20. Congruent • In Geometry, two objects that have • The same size and • The same shape are called congruent. What are some objects in the classroom that are congruent?

  21. Congruent __________ • Segments (1.3) • Angles(1.4) • Triangles(ch.4) • Circles(ch.9) • Arcs(ch.9)

  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 • Based on the diagram, what does this mean? • 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. Something that is going to cut directly through the 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.

  30. Ch. 1 Quiz Know the following… • Definition of equidistant • Real world example of points, lines, planes • Types of intersections • Points, lines, planes • Characteristics • Mathmatical notation

More Related