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. 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 Symbols Name

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. H G E C D A Example 1 Use the diagram above. What is the intersection of plane HGC and plane AED?

8. Use the diagram to determine the intersection of AD and CD. Example 2 Example 3 Use the diagram below. What is the intersection of plane FBC and plane EHG? is the intersection between the lines

9. K V JC 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 Ray JC J

10. Definitions • Opposite rays – two collinear rays with the same endpoint • Form a line • • • Ray VK Ray VC C V K Parallel lines – coplanar lines that do not intersect Skew lines – lines that are not parallel and do not intersect