Transcript 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: AB
– No arrows on the end of a line.
– Reads: Line segment (or segment) 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: AB
– Reads: Ray AB
– The ray continues on past B indefinitely
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
Q
R
Endpoints
S
Examples of Opposite Rays
Ex.1: Naming segments and rays.
L
P
• Name 3 segments:
– LP
– PQ
– LQ
Are LP and PL opposite rays??
No, not the same endpoints
Q
• Name 4 rays:
– LQ
– QL
– PL
– LP
– PQ
Group Work
• Name the following line.
XY or YZ or ZX
Z
• Name a segment.
XY or YZ or XZ
Y
• Name a ray.
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
I want a real
number as the
answer
Length of MJ
• 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, oneto-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.
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.
Segment Addition Postulate
• Student demonstration
• If B is between A and C, then AB + BC =
AC.
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
B
Write out the problem based
on the segments, then
substitute in the info
C
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.
3
3
A
P
B
Bisector of a segment
• A line, segment, ray or plane that
intersects the segment at its midpoint.
3
3
A
B
P
Something that is
going to cut
directly through
the midpoint
Remote time
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…
1. Definition of equidistant
2. Real world example of points, lines,
planes
3. Types of intersections
4. Points, lines, planes
1. Characteristics
2. Mathmatical notation