4.4 Equidistant Theorem

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• 4.4 Equidistant Theorem
• Objectives
• Use the equidistant theorem to prove
  perpendicular bisectors

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distance the shortest length between two
objects Postulate A line segment is the
shortest distance between 2 points
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If two points P and Q are the same distance from
a third point X, then X is said to be equidistant
from P and Q.
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The perpendicular bisector of a segment is the
line that bisects and is perpendicular to the
segment. Conditional Statement If a segment is
a perpendicular bisector, then it bisects and is
perpendicular to the segment. Converse If a
segment is perpendicular to and bisects a
segment, then it is the perpendicular bisector of
the segment.
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Thm. 24 If two points are each equidistant from
the endpoints of a segment, then the two points
determine the perpendicular bisector of that
segment.
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Thm. 25 If a point is on the perpendicular
bisector of a segment, then it is equidistant
from the endpoints of a segment.
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