Geometry Section 1-1 1112

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Geometry Section 1-1 1112

  1. 1. CHAPTER 1 Tools of Geometry
  2. 2. SECTION 1-1 Points, Lines, and Planes
  3. 3. ESSENTIAL QUESTIONS How do you identify and model points, lines, and planes? How do you identify intersecting lines and planes?
  4. 4. VOCABULARY 1. Undefined Term: 2. Point: 3. Line:
  5. 5. VOCABULARY 1. U n d e fi n e d T e r m : The things in Geometry that can really only be explained in examples and descriptions 2. Point: 3. Line:
  6. 6. VOCABULARY 1. U n d e fi n e d T e r m : The things in Geometry that can really only be explained in examples and descriptions 2. P o i n t : A location in space with no shape or size; noted as a capital letter 3. Line:
  7. 7. VOCABULARY 1. U n d e fi n e d T e r m : The things in Geometry that can really only be explained in examples and descriptions 2. P o i n t : A location in space with no shape or size; noted as a capital letter 3. L i n e : An infinite number of points that together have no thickness or width; need two points to determine the line; use either a lowercase letter or AB
  8. 8. VOCABULARY 4. Plane: 5. Collinear: 6. Coplanar: 7. Intersection:
  9. 9. VOCABULARY 4. P l a n e : A flat surface with at least three points that goes on forever in all directions; three points determine a plane; Often a capital script letter 5. Collinear: 6. Coplanar: 7. Intersection:
  10. 10. VOCABULARY 4. P l a n e : A flat surface with at least three points that goes on forever in all directions; three points determine a plane; Often a capital script letter 5. C o l l i n e a r : Points that lie on the same line 6. Coplanar: 7. Intersection:
  11. 11. VOCABULARY 4. P l a n e : A flat surface with at least three points that goes on forever in all directions; three points determine a plane; Often a capital script letter 5. C o l l i n e a r : Points that lie on the same line 6. C o p l a n a r : Points that lie in the same plane 7. Intersection:
  12. 12. VOCABULARY 4. P l a n e : A flat surface with at least three points that goes on forever in all directions; three points determine a plane; Often a capital script letter 5. C o l l i n e a r : Points that lie on the same line 6. C o p l a n a r : Points that lie in the same plane 7. I n t e r s e c t i o n : Where two figures meet; this is the set of points they have in common
  13. 13. VOCABULARY 8. Definition: 9. Defined Terms: 10. Space:
  14. 14. VOCABULARY 8. D e fi n i t i o n : Explanations that are used based off of other undefined and defined terms 9. Defined Terms: 10. Space:
  15. 15. VOCABULARY 8. D e fi n i t i o n : Explanations that are used based off of other undefined and defined terms 9. D e fi n e d T e r m s : Another way of working with a definition 10. S p a c e : An infinite three-dimensional set of points
  16. 16. EXAMPLE 1 Use the figure to name each of the following. a. A line containing point R b. A plane containing point P
  17. 17. EXAMPLE 1 Use the figure to name each of the following. a. A line containing point R m, RT, RS, etc. b. A plane containing point P
  18. 18. EXAMPLE 1 Use the figure to name each of the following. a. A line containing point R m, RT, RS, etc. b. A plane containing point P A
  19. 19. EXAMPLE 2 Name the geometric shape modeled by each object. a. A crack in a sidewalk b. A drop of water on the sidewalk
  20. 20. EXAMPLE 2 Name the geometric shape modeled by each object. a. A crack in a sidewalk line b. A drop of water on the sidewalk
  21. 21. EXAMPLE 2 Name the geometric shape modeled by each object. a. A crack in a sidewalk line b. A drop of water on the sidewalk point
  22. 22. EXAMPLE 3 Draw and label plane T that contains lines UV and WX such that the lines intersect at point Z. Then, add a point H to plane T so that it is not collinear with either UV or WX.
  23. 23. EXAMPLE 3 Draw and label plane T that contains lines UV and WX such that the lines intersect at point Z. Then, add a point H to plane T so that it is not collinear with either UV or WX. Compare your drawings with a neighbor; discuss
  24. 24. EXAMPLE 4 Points A(−3, 3) and B(2, −5) form a line. Graph the points and line on the coordinate plane, then add a point C so that it is collinear with A and B.
  25. 25. EXAMPLE 4 Points A(−3, 3) and B(2, −5) form a line. Graph the points and line on the coordinate plane, then add a point C so that it is collinear with A and B.
  26. 26. EXAMPLE 4 Points A(−3, 3) and B(2, −5) form a line. Graph the points and line on the coordinate plane, then add a point C so that it is collinear with A and B. x y
  27. 27. EXAMPLE 4 Points A(−3, 3) and B(2, −5) form a line. Graph the points and line on the coordinate plane, then add a point C so that it is collinear with A and B. x y A
  28. 28. EXAMPLE 4 Points A(−3, 3) and B(2, −5) form a line. Graph the points and line on the coordinate plane, then add a point C so that it is collinear with A and B. x y A B
  29. 29. EXAMPLE 4 Points A(−3, 3) and B(2, −5) form a line. Graph the points and line on the coordinate plane, then add a point C so that it is collinear with A and B. x y A B
  30. 30. EXAMPLE 4 Points A(−3, 3) and B(2, −5) form a line. Graph the points and line on the coordinate plane, then add a point C so that it is collinear with A and B. x y A B C
  31. 31. EXAMPLE 5 Answer the following. a. How many points are need to form a line? b. How many points are needed to form a plane? c. What is the intersection of two planes? d. What is the intersection of two lines? e. What is the difference between collinear and coplanar?
  32. 32. PROBLEM SET
  33. 33. PROBLEM SET p. 8 #1-47 odd, 58 “In terms of being late or not starting at all, then it’s never too late.” - Alison Headley

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