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.