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CHAPTER 1

CHAPTER 1. SECTION 1-1. A Game and Some Geometry. SECTION 1-2. Points, Lines and Planes. POINT – it indicates a specific location and is represented by a dot and a letter, but it has no dimensions. • R • S • T.

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CHAPTER 1

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  1. CHAPTER 1

  2. SECTION 1-1

  3. A Game and Some Geometry

  4. SECTION 1-2 Points, Lines and Planes

  5. POINT– it indicates a specific location and is represented by a dot and a letter, but it has no dimensions • • R • S • • T

  6. LINE – is a set of points that extends without end in two opposite directions • R S • «—•—————•—» line RS

  7. PLANE – is a set of points that extends in all directions along a flat surface • • Y W

  8. COLLINEAR POINTS – points that lie on the same line F • C D E « » • • •

  9. COPLANAR POINTS – are points that lie in the same plane E • • B C • A • • D

  10. « P » • « » INTERSECTION – set of all points common to two geometric figures

  11. SECTION 1-3 Segments, Rays and Distances

  12. « » • • J K RAY – a part of a line that begins at one point, called the ENDPOINT and extends without end in one direction

  13. • • F G LINE SEGMENT - part of a line that begins at one endpoint and ends at another

  14. POSTULATES - accepted as true without proof

  15. RULER POSTULATE The points on any line can be paired with the real numbers in such a way that any point can be paired with 0 and any other point can be paired with 1.

  16. The real number paired with each point is the coordinate of that point. The distance between any two points on the line is equal to the absolute value of the difference of their coordinates.

  17. THE SEGMENT ADDITION POSTULATE If point B is between points A and C, then AB +BC = AC

  18. AC = 47, AB = n – 5, and BC = n + 8, Find AB • • • A B C Given the figure below:

  19. AC = AB + BC 47 = (n – 5) + (n + 8) 47 = 2n + 3 44 = 2n 22 = n, therefore AB = 22-5 or 17

  20. • • J K Congruent segments segments that are equal in length 12 12 S R

  21. MIDPOINT– the point that divides a segment into two segments of equal length.

  22. BISECTOR of a SEGMENT– is any line, segment, ray, or plane that intersects the segment at its midpoint. M R • • S

  23. SECTION 1-4Angles

  24. ANGLE– the union of two rays with a common endpoint. The rays are called sides VERTEX –endpoint of an angle A • B • • C C

  25. PROTRACTOR POSTULATE Let O be a point on AB such that O is between A and B. Then ray OA can be paired with O° and ray OB can be paired with 180°

  26. P • Q • 180º 0º • • • O A B

  27. If OP is paired with x and OQ is paired with y, then the number paired with measure of angle POQ is | x – y |. This is called the measure of angle POQ.

  28. ANGLE ADDITION POSTULATE If point B lies in the interior of angle AOC, then: mAOB + m BOC = m AOC

  29. A • B • C O •

  30. CONGRUENT ANGLES angles that have equal measures 40° 40°

  31. ADJACENT ANGLES two angles in the same plane that share a common side and a common vertex, but have no interior points in common

  32. ADJACENT ANGLES A • B • C O • AOB and BOC

  33. BISECTOR of an ANGLE is the ray that divides the angle into two congruent adjacent angles.

  34. A • B • C O • M AOB = M BOC

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

  36. 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 four points not all in one plane.

  37. POSTULATE 6 • Through any two points there is exactly one line (Two points determine a line)

  38. Through any three points, there is at least one plane, and through any three noncollinear points there is exactly one plane. POSTULATE 7

  39. • • E F • • G

  40. POSTULATE 8 • If two points are in a plane, then the line that contains the points is in that plane.

  41. • • E • G

  42. POSTULATE 9 • If two planes intersect, then their intersection is a line

  43. K • W U • J

  44. THEOREMS – Statements that have been proven.

  45. If two lines intersect, then they intersect in exactly one point. THEOREM 1-1

  46. « » • • A B P •

  47. Through a line and a point not in the line there is exactly one plane. THEOREM 1-2

  48. If two lines intersect, then exactly one plane contains the lines. THEOREM 1-3

  49. • F • E • G D

  50. THE END

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