SOME THEOREMS AND POSTULATES

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• SOME THEOREMS AND POSTULATES
• Fernando Rodriguez
• Buena Park HS
• frodriguez_at_fjuhsd.k12.ca.us
• Presented at CMC South
• Palm Springs, CA
• Nov. 4, 2005

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Postulate 2 Segment Addition Postulate

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

AC

A
C
B
BC

AB
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A segment bisector is a segment, ray, line, or
plane that intersects a segment at its midpoint.
M is the midpoint of if M is on
and AM MB.
is a bisector of .
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Bisecting An Angle

• An angle bisector is a ray that divides an angle
  into two adjacent angles that are congruent. In
  the diagram ray bisects because
  it divides the angle into two congruent angles,
  _____ and _____.

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To write AB is Parallel to CD
A
B
D
C
you write AB CD
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Parallel and Perpendicular Postulates
POSTULATE 13 Parallel Postulate If there is a
line and a point not on the line, then there is
exactly one line through the point parallel to
the given line.
P
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Parallel and Perpendicular Postulates
POSTULATE 14 Perpendicular Postulate If there is
a line and a point not on the line, then there is
exactly one line through the point perpendicular
to the given line.
P
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Warm-Up
a.
b.
c.
d.
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Theorem 5.9 Midsegment theorem The segment
connecting the midpoints of two sides of a
triangle is parallel to the third side and half
as long