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1-5 Postulates and Theorems Relating Points, Lines and Planes

1-5 Postulates and Theorems Relating Points, Lines and Planes. Postulate. A line contains at least two points, a plane contains at least 3 points not all in one line; space contains at least four points not all in one plane. Postulate. Through any two points there is exactly one line.

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1-5 Postulates and Theorems Relating Points, Lines and Planes

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  1. 1-5Postulates and Theorems Relating Points, Lines and Planes

  2. Postulate • A line contains at least two points, a plane contains at least 3 points not all in one line; space contains at least four points not all in one plane.

  3. Postulate • Through any two points there is exactly one line.

  4. Postulate • Through any 3 points there is at least one plane, and through any three noncollinear points there is EXACTLY one plane.

  5. Postulate • If two points are in a plane, then the line that contains the points is in the plane.

  6. Postulate • If two planes intersect, then their intersection is a line.

  7. A line contains at least two points, a plane contains at least 3 points not all in one line; space contains at least for points not all in one plane. • Through any two points there is exactly one line. • Through any 3 points there is at least one plane, and through any three noncollinear points there is EXACTLY one plane. • If two points are in a plane, then the line that contains the points is in the plane. • If two planes intersect, then their intersection is a line.

  8. What is a theorem? • Important statements that have been PROVEN TRUE. From previous information

  9. Theorem • If 2 lines intersect, then they intersect in exactly one point.

  10. Theorem • Through a line and a point not in the line there is exactly one plane.

  11. Theorem • If 2 lines intersect, then exactly one plane contains the lines.

  12. Homework • Pg. 25 #s 5-17, 20 • Pg. 30 #s 5-20

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