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Chapter 1-5

Chapter 1-5. Postulates and Theorems Relating to Points, Lines, and Planes p. 22. Postulates and Theorems. Postulates- assumptions accepted without proof Theorems- statements that are justified through arguments (proved) Postulates are used to prove theorems. Postulates- Review.

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Chapter 1-5

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  1. Chapter 1-5 Postulates and Theorems Relating to Points, Lines, and Planes p. 22

  2. Postulates and Theorems • Postulates- assumptions accepted without proof • Theorems- statements that are justified through arguments (proved) • Postulates are used to prove theorems

  3. Postulates- Review • Ruler Postulate (1) • Points on a line can be paired with real numbers in such a way that any two points can have coordinates 0 and 1. • Once a coordinate system has been chosen this way, the distance between any two points equals the absolute value of the difference of their coordinates.

  4. Postulates- Review • Protractor Postulate (3) • On AB choose any point O between A and B • Consider rays OA and OB and all other rays drawn from O on one side of AB • Rays can be paired with real numbers from 1 to 180 such that… • OA is paired with 0 and OB is paired with 180 and • If OP is paired with x, and OQ with y, then m POQ = |x – y|

  5. Postulates- Review • Segment Addition Postulate (2) • If B is between A and C, then • AB + BC = AC • Angle Addition Postulate (4) • If point B lies in the interior of AOC, then • m AOB + m BOC = m AOC • If AOC is a straight angle and B is any point not on AC, then • m AOB + m BOC = 180

  6. More Postulates • Postulate 5- • A line contains at least two points • A plane contains at least three points not all in one line • Space contains at least 4 points not all in one plane

  7. And More Postulates • Postulate 6- Through any two points, there is exactly one line • Postulate 7- Through any three points, there is at least one plane and through any three noncollinear points there is exactly one plane

  8. And Even More Postulates • Postulate 8- If two points are in a plane, then the line that contains the points is in that plane • Postulate 9- If two planes intersect, then their intersection is a line

  9. Theorems • Theorem 1-1- If two lines intersect, then they intersect at exactly one point • Theorem 1-2- Through a line and a point not in the line, there is exactly one plane • Theorem 1-3- If two lines intersect, then exactly one plane contains the lines • “Exactly one” = one and only one

  10. Homework

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