Chapter 5 Properties of Triangles Perpendicular and Angle Bisectors Sec 5.1

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Chapter 5 Properties of Triangles Perpendicular
and Angle BisectorsSec 5.1

• Goal
• To use properties of perpendicular bisectors and
  angle bisectors

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Perpendicular Bisector
Perpendicular Bisector a segment, ray, line, or
plane that is perpendicular to a segment at its
midpoint.
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Equidistant
Equidistant from two points means that the
distance from each point is the same.
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Perpendicular Bisector Theorem
Perpendicular Bisector Theorem If a point is on
the perpendicular bisector of a segment, then it
is equidistant from the endpoints of the segment.
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Converse of the Perpendicular Bisector Theorem
Converse of the Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a
segment, then it is on the perpendicular bisector
of a segment.
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Example
Does D lie on the perpendicular bisector of
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Example
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Distance from a point to a line
The distance from a point to a line is defined to
be the shortest distance from the point to the
line. This distance is the length of the
perpendicular segment.
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Angle Bisector Theorem
Angle Bisector Theorem If a point (D) is on
the bisector of an angle, then it is equidistant
from the two sides of the angle.
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Converse of the Angle Bisector Theorem
Converse of the Angle Bisector Theorem If a
point is on the interior of an angle, and is
equidistant from the sides of the angle, then it
lies on the bisector of the angle.
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Examples
Does the information given in the diagram allow
you to conclude that C is on the perpendicular
bisector of AB?
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Examples
Does the information given in the diagram allow
you to conclude that P is on the angle bisector
of angle A?
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Examples
Draw the segment that represents the distance
indicated.
R perpendicular to LM
T perpendicular to AP
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Examples
Name the segment whose length represents the
distance between M to AT T to HM H to MT