Warmup

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Prove that seg PA ≅ seg PB.

Definition: The distance between two objects is the length of the shortest path between them.

Postulate: A line is the shortest path between two points.

Definition: If a point is the same distance from two different points, it is equidistant from them.

Definition: The perpendicular bisector of a segment is the line that bisects and is perpendicular to that segment.

Theorem 25

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

Theorem 24

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) If two points are each equidistant from the endpoints of a segment, then the two points determine the perpendicular bisector of that segment.

Sample problem 2

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Given: △ABC is isosceles, with seg AB ≅ seg AC, and E is the midpoint of seg BC.

Prove: seg AE ⊥ seg BC

	△ABC is isosceles, with seg AB ≅ seg AC	Given
	E is the midpoint of seg BC.	Given
	seg BE ≅ seg EC	Definition of midpoint
	Seg AE ⊥ seg BC	Equidistance theorem: Two points each equidistant form the endpoints of a segment determine the perpendicular bisector of the segment.