Warm – up
True / false : If false, explain why
•
•
•
•
Collinear points are coplanar
Planes have edges
Two planes intersect in a line segment
Two intersecting lines meet in exactly one
point
• Line XY can be denoted as XY or YX.
• A line has one endpoint
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
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
Are XY and YX
opposite rays??
No, not the
same endpoints
Number Lines
• On a number line every point (LETTER) is
paired with a coordinate (NUMBER)
– What is the coordinate of each letter?
K
M
J
What is the Length of MJ?
• When I write MJ it means “The length MJ”
– It is the distance between point M and point J.
– Length/distance is always positive!!
• FIND MJ
K
M
J
Questions 1 -9
-
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 markings for segments and angles
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
Questions 10, 11 15 – 20, 12
Definition: Midpoint of a
segment
• Based on the diagram, what does this
mean?
• The point that divides the segment into
two congruent segments.
3
3
B
P
A
What marking do we use to show congruent segments?
Definition: 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
Marking diagram with given
information
• P. 15 – problems 5 – 18
• P. 16 – 33 - 36
Postulates
• 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…..
• Learn them!
– Unless it has a name (i.e. “Ruler Postulate”)
– Not “Postulate 6”
• named different in every text book
Segment Addition Postulate
• Student demonstration
• If B is between A and C, then AB + BC =
AC.
Example 1
• Use the rule for segment addition
postulate to set up an equation
Write out the problem based
on the segments, then
substitute in the info
Example 2
• Use the rule for midpoint to set up an
equation
– B is the midpoint of segment AC
A- Sometimes
B – Always
C - Never
• A bisector of a segment is ____________
a line.
• A ray _______ has a midpoint.
• Congruent segments ________ have
equal lengths.
• 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 (drawings)
4. Points, lines, planes
1. Characteristics
2. Mathematical notation