1 5 Postulates And Theorems Relating Points, Lines Filled In

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1 5 Postulates And Theorems Relating Points, Lines Filled In

  1. 1. Postulates and Theorems Relating Points, Lines, and Planes 1-5
  2. 2. Recall… <ul><li>4 Postulates we’ve accepted so far: </li></ul><ul><ul><li>The Ruler Postulate </li></ul></ul><ul><ul><li>The Protractor Postulate </li></ul></ul><ul><ul><li>The Segment Addition Postulate </li></ul></ul><ul><ul><li>The Angle Addition Postulate </li></ul></ul>
  3. 3. More Postulates!!! <ul><ul><li>Postulate 5: </li></ul></ul><ul><ul><li>A line contains at least ___ points </li></ul></ul><ul><ul><li>A plane contains at least ___ non collinear points </li></ul></ul><ul><ul><li>space contains at least ___ points not all in one plane. </li></ul></ul>
  4. 4. More Postulates!!! <ul><li>Postulate 6: </li></ul><ul><ul><li>Through any ___ points, there is exactly one line </li></ul></ul><ul><li>Postulate 7: </li></ul><ul><ul><li>Through any 3 points there is at least __ plane, and through any three non collinear points there is exactly ____ plane. </li></ul></ul>
  5. 5. More Postulates!!! <ul><ul><li>Postulate 8 </li></ul></ul><ul><ul><ul><li>If two points are in a plane, then the line that contains the points is in that plane. </li></ul></ul></ul>A B M
  6. 6. More Postulates!!! <ul><ul><li>Postulate 9 </li></ul></ul><ul><ul><ul><li>If two planes intersect, then their intersection is a line. </li></ul></ul></ul><ul><ul><ul><ul><li>DC is the intersection of Plane A and Plane B </li></ul></ul></ul></ul>A B
  7. 7. Theorems <ul><li>Important statements that are proved are called theorems . </li></ul><ul><ul><li>May be used to justify statements </li></ul></ul>
  8. 8. Theorems <ul><li>Theorem 1-1: Intersection of lines </li></ul><ul><ul><li>If two lines intersect, then they intersect in exactly one point. </li></ul></ul>
  9. 9. Theorems <ul><li>Theorem 1-2 </li></ul><ul><ul><li>Through a line and a point not in the line there is exactly one plane. </li></ul></ul>B K A
  10. 10. Theorems <ul><li>Theorem 1-3 </li></ul><ul><ul><li>If two lines intersect, then exactly one plane contains the lines. </li></ul></ul>
  11. 11. SPICSA <ul><li>Pg 25, # 1 – 11, 13 - 15, 18, 19 a-d </li></ul>

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