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4.4 Equidistant Theorem Objective: Use the equidistant theorem to prove perpendicular bisectors

4.4 Equidistant Theorem Objective: Use the equidistant theorem to prove perpendicular bisectors. Distance: the shortest length between two objects. Postulate : A line segment is the shortest distance between two points. X. P. Q.

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4.4 Equidistant Theorem Objective: Use the equidistant theorem to prove perpendicular bisectors

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  1. 4.4 Equidistant Theorem Objective: • Use the equidistant theorem to prove perpendicular bisectors

  2. Distance:the shortest length between two objects. Postulate: A line segment is the shortest distance between two points.

  3. X P Q If two points P and Q are the same distance from a point X, then X is said to be equidistant from P and Q.

  4. The perpendicularbisectorof a segment is the line that bisects and is perpendicular to the segment.

  5. Theorem 24: If two points are each equidistant from the endpoints of a segment, then the two points determine the perpendicular bisector of that segment.

  6. Theorem 25: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of a segment.

  7. Q Example 1: 2 1 R T 3 4 U S 1  2 Given 3  4 Given

  8. D Example 2: E A C B Given  Bisector Theorem  Bisector Theorem Reflexive Property ∆ADC ∆ABC SSS

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