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5.2 Perpendicular and Angle Bisectors

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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  1. 5.2 Perpendicular and Angle Bisectors • A point is equidistant from two objects if it is the same distance from the objects.

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

  3. 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.

  4. 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

  5. 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.

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

  7. 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.

  8. 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

  9. More Practice!!!!! • Homework – Textbook p. 296 – 297 #6 – 22.

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