1'5 Division of Segments and Angles

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1.5 Division of Segments and Angles 8
Definitions Bisection of segments conditional
If a point (or segment, ray, or line) bisects a
segment, then the point divides the segment into
2 congruent segments. converse If a point (or
segment, ray, or line) divides a segment into 2
congruent segments, then the point bisects the
segment. Midpoint conditional If a point is
the midpoint of a segment, then the point divides
the segment into 2 congruent segments. converse
If a point divides a segment into 2 congruent
segments, then the point is the midpoint of the
segment.
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Trisection of segments conditional If 2 points
(or segments, rays, or lines) trisect a segment,
then the points divide the segment into 3
congruent segments. converse If 2 points (or
segments, rays, or lines) divide a segment into 3
congruent segments, then the points trisect the
segment. Trisection points conditional
If 2 points are the trisection points of a
segment, then the points divide the segment into
3 congruent segments. converse If 2 points
divide a segment into 3 congruent segments, then
the points are the trisection points of the
segment.
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Angle bisection conditional If a ray bisects
an angle, then the ray divides the angle into 2
congruent angles. converse If a ray divides
an angle into 2 congruent angles, then the ray
bisects the angle.
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Angle trisection conditional If 2 rays trisect
an angle, then the rays divide the angle into 3
congruent angles. converse If 2 rays divide an
angle into 3 congruent angles, then the rays
trisect the angle.