Warm-up Open your books to page 11 –Look through the bold face terms in sec. 1.3 –Look at the diagrams that go with each term You will need to be ready to answer questions in relation to these terms for the lesson

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 AB

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 A B AB AB

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

Examples of Opposite Rays

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

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

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

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

Length of MJ When I write MJ = “The length MJ” It is the distance between point M and point J. JKM I want a real number as the answer

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

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

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)

Remote time

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

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

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

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

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) A C B Write out the problem based on the segments, then substitute in the info

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?

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

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

Midpoint of a segment Based on the diagram, what does this mean? The point that divides the segment into two congruent segments. A B P 3 3

Bisector of a segment A line, segment, ray or plane that intersects the segment at its midpoint. A B P 3 3 Something that is going to cut directly through the midpoint

Remote time

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

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

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

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

Ch. 1 Quiz Know the following… 1.Definition of equidistant 2.Real world example of points, lines, planes 3.Types of intersections (drawings) 4.Points, lines, planes 1.Characteristics 2.Mathematical notation