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12 Cards in this Set
- Front
- Back
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Postulate 1
Ruler Postulate |
1) The points on a line can be paired with real numbers in such a way that any 2 points can have coordinates 0 and 1
2) Once a coordinate system has been chosen in this way, the distance between any 2 points equals the absolute value of the difference of their coordinates |
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Postulate 2
Segment Addition Postulate |
If B is between A and C, then
AB + BC = AC |
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Postulate 3
Protactor Postulate |
On line AB in a given plane, choose any point O between A&B. Consider ray OA&OB&all the rays that can be drawn from O on one side of line AB. These rays can be paired w/real numbers from 0 to 180 in such a way that:
a) Line OA is paired w/0 & line OB w/180 b) If ray OP is paired w/x and ray OP w/y, then m∠POQ = |x-y| |
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Postulate 4
Angle Addition Postulate |
If point B lies in interior of point AOC, then
m∠AOB + m∠BOC = m∠AOC If angle AOC is a straight angle and B is any point not on line AC, then m∠AOB + m∠BOC = 180 |
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Postulate 5
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- line contains at least 2 points
- plane contains at least 3 points not all in one line - space contains at least 4 points not all in on plane |
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Postulate 6
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Through any 2 points there is exactly 1 line
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Postulate 7
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- through any 3 points there is at least 1 plane
- through any 3 noncollinear points there is exactly 1 plane |
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Postulate 8
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If 2 points are in a plane, then the line that contains those points is in that plane
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Postulate 9
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If 2 planes intersect, then their intersection is a line
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Theorem 1-1
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If 2 lines intersect, then they intersect at exactly 1 point
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Theorem 1-2
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Through a line and a point, there is exactly 1 plane
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Theorem 1-3
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If 2 lines intersect, exactly 1 plane contains the lines
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