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Chapter 1

Chapter 1. Reasoning in Geometry. Section 1-1. Patterns and inductive reasoning. Inductive Reasoning. When you make a conclusion based on a pattern of examples or past events. Conjecture. A conclusion that you reach based on inductive reasoning. Counterexample.

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Chapter 1

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  1. Chapter 1 Reasoning in Geometry

  2. Section 1-1 Patterns and inductive reasoning

  3. Inductive Reasoning When you make a conclusion based on a pattern of examples or past events

  4. Conjecture A conclusion that you reach based on inductive reasoning

  5. Counterexample An example that shows your conjecture is false It only takes one counterexample to prove your conjecture false

  6. Examples Find the next three terms of each sequence. 11.2, 9.2, 7.2, ……. 1, 3, 7, 13, 21, ……. ……..

  7. Section 1-2 Points, lines and planes

  8. Point A basic unit of geometry Has no size Named using capital letters

  9. Line A series of points that extends without end in two directions. Named with a single lowercase letter or by two points on the line

  10. Collinear and Noncollinear Points that lie on the same line Points that do not lie on the same line

  11. Ray Has a definite starting point and extends without end in one direction Starting point is called the endpoint Named using the endpoint first, then another point

  12. Line Segment Has a definite beginning and end Part of a line Named using endpoints

  13. Plane A flat surface that extends without end in all directions Named with a single uppercase script letter or three noncollinear points

  14. Coplanar and Noncoplanar Points that lie in the same plane Points that do not lie in the same plane

  15. Section 1-3 postulates

  16. Postulates Facts about geometry that are accepted as true

  17. Postulate 1-1 Two points determine a unique line

  18. Postulate 1-2 If two distinct lines intersect, then their intersection is a point.

  19. Postulate 1-3 Three noncollinear points determine a unique plane.

  20. Postulate 1-4 If two distinct planes intersect, then their intersection is a line.

  21. Section 1-4 Conditional statements and their converses

  22. Conditional Statement Written in if-then form Examples: Ifpoints are collinear, then they lie on the same line. Ifa figure is a triangle,then it has three angles. If two lines are parallel, then they never intersect.

  23. Hypothesis The part following the if If points are collinear, then they lie on the same line. If a figure is a triangle,then it has three angles. If two lines are parallel, then they never intersect.

  24. Conclusion The part following the then If points are collinear, then they lie on the same line. Ifa figure is a triangle,then it has three angles. If two lines are parallel, thenthey never intersect.

  25. Converse A conditional statement is formed by exchanging the hypothesis and the conclusion in a conditional statement

  26. Example Statement: If a figure is a triangle, then it has three angles. Converse: If a figure has three angles, then it is a triangle.

  27. Section 1-6 A plan for problem solving

  28. Perimeter The distance around a figure

  29. Formula An equation that shows how certain quantities are related

  30. Area The number of square units needed to cover the surface of a figure

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