Section 1.1 – The Building Blocks of Geometry

 

Undefined Terms

 

Points are collinear if a single line can contain them all. 

          -   Any 2 points are collinear

 

                             

Points are coplanar if a single plane can contain them all.

          -  Any 3 points are coplanar

 

Definitions:

 

Segment – a part of a line that begins at one point and ends at another point.  The points are called endpoints of the segment.

 

          A and B are the endpoints of the segment

 

Ray – a part of a line that starts at a point and extends infinitely in one direction.  The point is called the endpoint of the ray.

 

         A is the endpoint

 

Angle – a figure formed by two rays with a common endpoint.  The common endpoint is called the vertex of the angle and the rays are the sides of the angle.

                                                                                 

 

 

                                                                 ,  ,

                                                                 B is vertex

 

vertex
 
 

 

 


See examples on page 11 in the textbook.

 

When geometric figures have one or more points in common, they are said to intersect.  The set of points they have in common is called their intersection.

 

Postulate – statements accepted as true without proof

 

Postulates:

 

1.      The intersection of two lines is a point.

2.      The intersection of two planes is a line.

3.      Through any two points there is exactly one line.

4.      Through any three noncollinear points there is exactly one plane

5.      If two points are in a plane, then the line containing them is in the same plane.