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# Definitions Chapter 1

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### Definitions Chapter 1

1. 1. Definitions Chapter 1 Inductive reasoning Conjecture Counterexample
2. 2. Definitions <ul><li>Inductive reasoning </li></ul><ul><ul><li>Reasoning that is based on patterns you observe </li></ul></ul><ul><ul><li>Example </li></ul></ul><ul><ul><ul><li>Find a pattern for each sequence. Use the pattern to find the next term </li></ul></ul></ul><ul><ul><ul><li>384, 192, 96, 48, ______ </li></ul></ul></ul>
3. 3. Definitions continued <ul><li>Conjecture </li></ul><ul><ul><li>A conclusion that is made based on inductive reasoning </li></ul></ul><ul><li>Counterexample </li></ul><ul><ul><li>An example for which a conjecture is incorrect </li></ul></ul>
4. 4. Definitions <ul><li>Point – a location (no size) </li></ul><ul><li>Line – a set of points that extends in opposite direction without end </li></ul><ul><li>Collinear points – points that lie on the same line </li></ul><ul><li>Plane – a flat surface with no thickness and extends without end </li></ul><ul><li>Coplanar – points that lie in the same plane </li></ul><ul><li>Postulate – an excepted statement of fact </li></ul>
5. 5. Symbols Name <ul><li>Line – </li></ul><ul><li>or line m </li></ul><ul><li>Plane – Plane XYZ </li></ul><ul><li>or Plane R </li></ul><ul><li>Small dot with capital letter </li></ul><ul><li>Use any two points or single lower case letter </li></ul><ul><li>At least 3 noncollinear points or a captial letter </li></ul>
6. 6. Postulates <ul><li>1-1 – Through any two points there is exactly one line </li></ul><ul><li>1-2 – If two lines intersect, then they intersect in exactly one point. </li></ul><ul><li>1-3 – If two planes intersects, then they intersect in exactly one line </li></ul><ul><li>1-4 – Through any three noncollinear points there is exactly one plane </li></ul>
7. 7. G C H D E A Use the diagram above. What is the intersection of plane HGC and plane AED ? Example 1
8. 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. 9. Definitions <ul><li>Segment – a part of a line consisting of two endpoints and all points between them </li></ul><ul><li>Ray – part of a line that consists of one endpoint and all points of a line to one side of the endpoint </li></ul>• • Segment KV • C J Ray JC • K V JC
10. 10. Definitions <ul><li>Opposite rays – two collinear rays with the same endpoint </li></ul><ul><ul><li>Form a line </li></ul></ul>• 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