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Postulate: Segment Addition Postulate
Point B is a point on segment AC, i.e. B is between A and C,
if and only if
AB + BC = AC
The Segment Addition Postulate is often used in geometric
proofs to designate an arbitrary point on a segment. By choosing
a point on the segment that has a certain relationship to other
geometric figures, one can usually facilitate the completion of
the proof in question.
Congruent segments are segments with equal lengths. In the
above figure, AB and CD have the same length and are therefore
congruent. This is denoted as AB = CD or AB @
CD
(" @ " means "is
congruent to").
The midpoint of a segment is the point that divides the
segment into two congruent segments. Since AB = CD, then C is the
midpoint of segment AB.
The bisector of a segment is a line, plane, ray or another
segment that intersects the segment at its midpoint. Since DC
passes through C, the midpoint of AB, then DC is a bisector of segment
AB.
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