1.3 Segments, Rays, and Distance

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1.3 Segments, Rays, and Distance
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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
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• 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
A
B
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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
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Examples of Opposite Rays
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Ex.1 Naming segments and rays.
L
P
Q

• Name 3 segments
• LP
• PQ
• LQ

• Name 4 rays
• LQ
• QL
• PL
• LP
• PQ

Are LP and PL opposite rays?? No, not the same
endpoints
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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
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Number Lines

• On a number line every point is paired with a
  number and every number is paired with a point.

J
K
M
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Number Lines

• In the diagram, point J is paired with 8
• We say 8 is the coordinate of point J.

J
K
M
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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.

J
K
M
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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.
J
K
M
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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

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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)

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Remote time
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A- Sometimes B Always C - Never

• The length of a segment is ___________ negative.

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A- Sometimes B Always C - Never

• If point S is between points R and V, then S
  ____________ lies on RV.

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A- Sometimes B Always C - Never

• A coordinate can _____________ be paired with a
  point on a number line.

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Segment Addition Postulate

• Student demonstration
• If B is between A and C, then AB BC AC.

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Example 1

• If B is between A and C, with AB x, BCx6 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
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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?

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Congruent __________

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

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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
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Midpoint of a segment

• Based on the diagram, what does this mean?
• The point that divides the segment into two
  congruent segments.

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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
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Remote time
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A- Sometimes B Always C - Never

• A bisector of a segment is ____________ a line.

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A- Sometimes B Always C - Never

• A ray _______ has a midpoint.

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A- Sometimes B Always C - Never

• Congruent segments ________ have equal lengths.

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A- Sometimes B Always C - Never

• AB and BA _______ denote the same ray.

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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