Geometry Notes

  • 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.