Transcript Conjectures
Conjectures aka: Theorems and Postulates Conjectures: Postulates and Theorems • Postulate: A statement that is accepted without proof. Usually these have been observed to be true but cannot be proven using a logic argument. • Theorem: A statement that has been proven using a logic argument. – Many theorems follow directly from postulates. • Throughout this textbook Postulates and Theorems are referred to as Conjectures. Conjectures Relating Points, Lines, and Planes • 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. Conjectures Relating Points, Lines, and Planes • Through any two points there is exactly one line. Conjectures Relating Points, Lines, and Planes • Through any three points there is at least one plane (if collinear), and through any three noncollinear points there is exactly one plane. Conjectures Relating Points, Lines, and Planes • If two points are in a plane, then the line that contains the points is in that plane. Conjectures Relating Points, Lines, and Planes • If two planes intersect, then their intersection is a line. Major Conjectures Relating Points, Lines, and Planes • If two lines intersect, then they intersect in exactly one point. • Through a line and a point not in the line there is exactly one plane. • If two lines intersect, then exactly one plane contains the lines. Time to ponder….. 1. Coplanar lines that do not intersect A. vertical B. parallel C. ray D. plane 2. A an infinite number of points that has two distinct end points A. bisect B. line segment C. intersect D. congruent Time to ponder….. 3. Any three or more points that lie in the same plane A. coplanar B. line C. plane D. collinear 4. Coplanar → Points on the same line True False 5. Line → one endpoint and extends indefinitely in one direction True False Time to ponder….. 6. Collinear → an infinite number of points that goes on forever in both directions True False 7. Plane → an infinite number of points that goes on forever in both directions True False Time to ponder….. 9. Give another names for plane S. 10. Name three collinear points. 11. Name the point of intersection of line AC and plane S. Time to ponder….. 12. The intersection of two lines is a ____________________ 13. The intersection of two planes is a ___________________ 14. Through any two points there is exactly one ___________ 15. Through any three non-collinear points there is exactly one _________________ 16. If two points are in a plane, then the line containing them _____________________ The End Once you study all the fancy words/vocabulary, Geometry is very easy to understand…so STUDY! You are Learning a new Language.