GEOMETRY
Legal Reasons
Level 1
Lines, Segments,
Rays, Distance How
to Play | Game
Levels | Reasons | Cards
| Game Board | Writing
Proofs |
1
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Point-Line-Plane Postulate
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- Unique Line Assumption: through any
two points there is exactly one line.
- Number Line Assumption: Every line is a set of points
that can be put into a one-to-one correspondence with the real
numbers, with any point on it corresponding to 0 and any other
point corresponding to 1.
- Dimension Assumption:
1.) Given a line in a plane, there is at least one point in the
plane that is not on the line.
2.) Given a plane in space, there is at least one point in space
that is not in the plane.
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2
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Line Intersection Theorem
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Two different lines intersect in at most one point.
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3
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Definition of Parallel Lines
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Two coplanar lines s and t are parallel lines, written
s//t, if and only if they have no points in common or they
are identical.
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4
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Definition of Betweenness
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A number is between two others, if it is greater than one of them
and less than the other is.
A point is between two other points if it is on the same line and
its coordinate is between their coordinates.
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5
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Definition of Segment
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The segment (or line segment) with endpoints A and B, denoted
is the set consisting of the distinct points A and B and all points
between A and B.
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6
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Definition of Ray
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The ray with endpoint A and containing a second point B, denoted
by ,
consists of the points on
and all points for which B is between each of them and A.
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7
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Definition of opposite rays
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and
are opposite rays if and only if A is between B and C.
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8
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The Distance Postulate
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- Uniqueness Property: On a line, there
is a unique distance between two points.
- Distance Formula: If two points on a line have coordinates
x and y, the distance between them is
|x - y|.
- Additive Property: If B is on ,
then
AB + BC = AC
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How
to Play | Game
Levels | Reasons | Cards
| Game Board | Writing
Proofs |