Definitions Chapter 1
- 1. Definitions Chapter 1 Inductive reasoning Conjecture Counterexample
- 2. Definitions Inductive reasoning Reasoning that is based on patterns you observe Example Find a pattern for each sequence. Use the pattern to find the next term 384, 192, 96, 48, ______
- 3. Definitions continued Conjecture A conclusion that is made based on inductive reasoning Counterexample An example for which a conjecture is incorrect
- 4. Definitions Point – a location (no size) Line – a set of points that extends in opposite direction without end Collinear points – points that lie on the same line Plane – a flat surface with no thickness and extends without end Coplanar – points that lie in the same plane Postulate – an excepted statement of fact
- 5. Symbols Name Line – or line m Plane – Plane XYZ or Plane R Small dot with capital letter Use any two points or single lower case letter At least 3 noncollinear points or a captial letter
- 6. Postulates 1-1 – Through any two points there is exactly one line 1-2 – If two lines intersect, then they intersect in exactly one point. 1-3 – If two planes intersects, then they intersect in exactly one line 1-4 – Through any three noncollinear points there is exactly one plane
- 7. G C H D E A Use the diagram above. What is the intersection of plane HGC and plane AED ? Example 1
- 8. Use the diagram below. What is the intersection of plane FBC and plane EHG ? is the intersection between the lines Example 2 Use the diagram to determine the intersection of AD and CD. Example 3
- 9. Definitions Segment – a part of a line consisting of two endpoints and all points between them Ray – part of a line that consists of one endpoint and all points of a line to one side of the endpoint • • Segment KV • C J Ray JC • K V JC
- 10. Definitions Opposite rays – two collinear rays with the same endpoint Form a line • V C Ray VK • K • Ray VC Parallel lines – coplanar lines that do not intersect Skew lines – lines that are not parallel and do not intersect