1.3 segments, rays, and distance
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
A B
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. End point always comes first.
– Ex: – Reads: Ray AB
A B
AB
• Opposite Rays – Are two collinear rays with the same endpoint. – Opposite rays always form a line.
– Ex:
Same Line
Q R S
RQ & RS
Endpoints
Ex.1: Naming segments and rays.
• Name 3 segments:– LP– PQ– LQ
• Name 4 rays:– LQ– QL– PL– LP– PQ
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.
X
Y
ZXY 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.
JK M
Number Lines
• In the diagram, point J is paired with 8
• We say 8 is the coordinate of point J.
JK M
Length of MJ
• The length MJ, is written MJ
• It is the distance between point M and point J.
JK M
Length of MJ
• You can find the length of a segment by subtracting the coordinates of its endpoints
JK M
• MJ = 8 – 5 = 3 • MJ = 5 - 8 = - 3
Either way as long as you take the absolute value of the answer.
Postulates and Axioms
• Statements that are accepted without proof
• Memorize all of them– Unless it has a name– Not “Postulate 6”
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.
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
• 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.
A
C
B
Congruent
• In Geometry, two objects that have– The same size and– The same shape
are called congruent.
Congruent __________
• Segments
• Angles
• Triangles
• Circles
• Arcs
Congruent Segments
• Have equal lengths
• To say that DE and FG have equal lengthsDE = FG
• To say that DE and FG are congruentDE FG
2 ways to say the exact same thing
Midpoint of a segment
• 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
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