Honors Geometry

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Honors Geometry

• Lesson 5.1
• Exploring Parts of Triangles

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What You Should LearnWhy You Should Learn It

• Goal 1 How to use properties of perpendicular
  bisectors
• Goal 2 How to use properties of angle bisectors
• Perpendicular bisectors and angle bisectors can
  be used to solve real-life problems such as in
  navigation or plumbing

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Lesson Investigation
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Perpendicular Bisector

• The Line CD is the perpendicular bisector of AB
  because it is perpendicular to AB, and it bisects
  AB

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Theorem 5.1Perpendicular 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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Theorem 5.2Perpendicular Bisector Converse

• If a point is equidistant from the endpoints of a
  segment, then it lies on the perpendicular
  bisector of the segment

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Distance between a Point and a Line

• The distance between a point and a line is the
  length of the perpendicular segment from the
  point to the line
• The distance between the point P and the line L
  is PO

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Lesson Investigation
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Theorem 5.3Angle Bisector Theorem

• If a point is on the bisector of an angle, then
  it is equidistant from the two sides of the angle

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Theorem 5.4Angle Bisector Converse

• If a point is in the interior of an angle and
  equidistant from the sides of an angle, then it
  lies on the bisector of the angle

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THE END