1.1. Points, Lines, and Planes http://www.ck12.org
a) How do the two planes intersect?
b) Is linelcoplanar with PlaneVorW?
c) AreRandQcollinear?
d) What point is non-coplanar with either plane?
e) List three coplanar points in PlaneW.
Solution:
a) In a line.
b) No.
c) Yes.
d)S
e) Any combination ofP,O,TandQwould be correct.
Further Beyond
With these new definitions, we can make statements and generalizations about these geometric figures. This section
introduces a few basic postulates. Throughout this book we will be introducing Postulates and Theorems so it is
important that you understand what they are and how they differ.
Postulates:Basic rules of geometry. We can assume that all postulates are true, much like a definition.
Theorem:A statement that can be proven true using postulates, definitions, and other theorems that have already
proven.
The only difference between a theorem and postulate is that a postulate isassumedtrue because it cannot be shown
to be false, a theorem must beproventrue. We will prove theorems later in this text.
Postulate 1-1:There is exactly one (straight) line through any two points.
Postulate 1-2:There is exactly one plane that contains any three non-collinear points.
Postulate 1-3:A line with points in a plane also lies within that plane.
Postulate 1-4:The intersection of two distinct lines will be one point.
Postulate 1-5:The intersection of two planes is a line.
When making geometric drawings, you need to be sure to be clear and label. For example, if you draw a line, be
sure to include arrows at both ends. Make sure you label your points, lines, and planes clearly, and refer to them by
name when writing explanations.
Example 7:Draw and label the intersection of line
←→
ABand ray−→
CDat pointC.