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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.
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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
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
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
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
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
Number Lines • On a number line every point is paired with a number and every number is paired with a point. K M J
Number Lines • In the diagram, point J is paired with 8 • We say 8 is the coordinate of point J. K M J
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
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
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)
A- Sometimes B – Always C - Never • The length of a segment is ___________ negative.
A- Sometimes B – Always C - Never • 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 B C Segment Addition Postulate • Student demonstration • If B is between A and C, then AB + BC = AC.
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
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
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.
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
A- Sometimes B – Always C - Never • 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.
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