Point an undefined term

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Point (an undefined term)

• Definition A location, represented by a dot.
  (a.k.a. vertex)
• Points are named using upper-case letters.
• The point where two lines cross is called a
  vertex.

Drawing Notation
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Line (an undefined term)

• Definition A straight path that extends in two
  directions (beyond the arrows). With 2 points,
  there is exactly one line that passes between
  them so a line is named using two points (which
  are uppercase) or a lowercase letter denoting the
  line.

Drawing Notation
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Ray

• Definition A line with one ending point (can be
  thought of as a starting point). NOTE For
  notation, always list the starting point followed
  by a point it goes through!
• Opposite rays have same starting point but
  opposite directions!

Drawing Notation
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Segments

• Definition A finite line with a starting point
  and an ending point (are interchangeable). It is
  also called a line segment.
• A segment is notated by 2 uppercase letters with
  a line above.
• The length of the segment is notated by the
  letters (no line!)

Drawing Notation
5
Plane (an undefined term)

• Definition A flat surface that extends without
  end. It is drawn using a quadrilateral (4-sided
  figure). A plane can be determined by just 3
  non-collinear points. It is named by 3 points on
  it (capital letters) or by one capital letter if
  named.

Drawing Notation
6
Intersection

• Definition The location where two geometric
  objects meet.
• Two lines (or rays or segments) intersect at a
  point
• Two planes intersect at a line.

Drawing Notation
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Collinear Coplanar

• Collinear points are collinear if they lie on
  the same line
• Coplanar points (or lines or rays or segments)
  are coplanar if they lie on the same plane

Drawing Notation
8
Segment Addition

• If two segments are collinear and share an
  endpoint (i.e.touch each other), then we can
  add their segment lengths to find the length of
  the entire segment.
• If B is between A and C, then AB BC AC

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Segment Addition Examples

• Use the diagram to find GH.
• Use the diagram to find EG.

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Congruent Segments

• Congruent equal in measure
• Two segments are congruent if they have the same
  length.
• We use the congruent symbol shown below. On the
  actual line segments, we use tick marks to
  represent congruency.
• If AB is congruent to CD,
• Then the length of AB equals the
  length of CD.

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Congruent Segments Examples

• Plot J (-3, 4), K (2, 4), L (1, 3), and M (1, -2)
  in a coordinate plane. Then determine whether JK
  and LM are congruent.

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Congruent Segments Examples

• In the diagram, points V, W, X, Y, and Z are
  collinear, VZ 52, XZ 20, and WX XY YZ.
  Find the indicated lengths.
• WX
• VW
• WY
• VX
• WZ
• VY

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Segment Bisector Midpoint

• A segment bisector is a point, ray, line, line
  segment, or plane that cuts a segment in half.
  The point where it bisects the segment is called
  the midpoint.
• Example M is the midpoint of AB.
• So, AM MB and AM MB.

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Segment Bisector/Midpoint Examples

• Ex Point M is the midpoint of VW. Find the
  length of VM.

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Midpoint Formula
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Midpoint Formula Other Method

• Another method for finding the midpoint of two
  points (or finding an endpoint given an endpoint
  and a midpoint) is
• Write the known points, one per line. On each
  line, write the vertex letter followed by the
  actual coordinates.
• If you need to find the midpoint, look for what
  is in the exact middle of the x-coordinates and
  repeat for the y-coordinates.
• If you need to find an endpoint, look at the
  pattern (adding or subtracting what number) to
  get from the x-coordinate of the given endpoint
  to the x-coordinate of the midpoint and then
  follow the pattern to find the x-coordinate of
  the other endpoint. Repeat for the y-coordinates.

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Midpoint Formula Example

• The endpoints of RS are R(1,-3) and S(4, 2).
  Find the coordinates of the midpoint M.

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Midpoint Formula Example

• The midpoint of JK is M(2,1). One endpoint is
  J(1,4). Find the coordinates of endpoint K.

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Three Properties of Equality

• Reflexive Property An object is equal to itself.
• Example If a5, then a5.
• Example For any segment AB, AB AB.
• Symmetric Property Each side of an equation is
  equal,
  no matter the order!
• Example If a5, then 5a.
• Example For any AB and CD If ABCD, then
  CDAB.
• Transitive Property Eliminate the middle man
  (like the
  Law of Syllogism).
• Example If ab and bc, then ac.
• Example If ABCD and CDEF, then ABEF.

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Three Properties of Equality Example

• Which of the following is an example of the
  Symmetric Property?
• A. If y x 4, then x 4 y.
• B. If x 3, then x 4 3 4.
• C. If x 3 y and y -4, then x 3 -4.
• D. x 3 x 3
• Identify the property that makes the statement
  true.
• If XY MN, then MN XY.
• If RS AB and if AB MN, then RS MN.