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5.1

5.1. Perpendicular and Angle Bisectors. Definitions. Distance from a point to a line: Length of the perpendicular segment from a point to a line. Equidistant: A point that is the same distance from two segments (rays or lines). . Angle Bisector Theorem. B.

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5.1

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  1. 5.1 Perpendicular and Angle Bisectors

  2. Definitions • Distance from a point to a line: • Length of the perpendicular segment from a point to a line. • Equidistant: • A point that is the same distance from two segments (rays or lines).

  3. Angle Bisector Theorem B • If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. A C D

  4. Example #1 L K H J

  5. Defn: Perpendicular Bisector • A line that is perpendicular to and bisects another segment. A C D B

  6. Perpendicular Bisector Theorem • If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. A E C D B

  7. Example #2 & 3 D M M Y C A B Y

  8. Example #4 A 2x + 3 y + 4 M T H ½ x + 8 3y

  9. Write eqn of perp bisector given two endpoints • STEPS: • 1) Find the midpoint of the segment • 2) Find the slope of the segment • 3) Find the slope of its perpendicular line • 4) Use the perpendicular slope and midpoint and plug into Point-Slope form 5) A ( 6, -3) B (0,5) 6) A (2, 7) B (-4, 3)

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