5 2 perpendicular and angle bisectors
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5.2 Perpendicular and Angle Bisectors PowerPoint PPT Presentation


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5.2 Perpendicular and Angle Bisectors. A point is equidistant from two objects if it is the same distance from the objects. 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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5.2 Perpendicular and Angle Bisectors

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5.2 Perpendicular and Angle Bisectors

  • A point is equidistant from two objects if it is the same distance from the objects.


Perpendicular Bisector Theorem

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


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 the segment.


Using the Perpendicular Bisector Theorem

  • What is the length of segment AB?

    BA = BC

    4x = 6x – 10

    -2x = -10

    x = 5

    AB = 4x

    AB = 4 (5)

    AB = 20


Distance from a Point to a Line

  • The distance from a point to a line is the length of the perpendicular segment from the point to the line.

    • Is also the length of the shortest segment from the point to the line.


Angle Bisector Theorem

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


Converse of the Angle Bisector Theorem

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


Using the Angle Bisector Theorem

  • What is the length of segment RM?

    RM = RP

    7x = 2x + 25

    5x = 25

    x = 5

    RM = 7x

    RM = 7 (5)

    RM = 35


More Practice!!!!!

  • Homework – Textbook p. 296 – 297 #6 – 22.


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