Geometry Theorems and Postulates for Line Systems
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The Old Double Cross
Theorems and Postulates for Line Systems

 

 The next group of definitions, postulates, and theorems

 has to do with our old pal the double cross.
 
 Let's review that double cross.
 Draw two parallel lines and a line that crosses them.
 Label all the angles with letters.
 Like this:
 

 
 We know two things about this.
 We know that:

 A = C = E = G   and   B = D = F = H

 
 We also know that:
 

If A = B = C = D, the crosses are perpendicular.

 

 
 Math types took this one little trick
 and turned it into a ton of definitions, theorems, and postulates
 (or axioms).
 
 DEFINITIONS:
 
 INTERIOR ANGLES
 The angles between the parallel lines.
 

 
 Angles B, C, E, and H are Interior Angles.
 
 EXTERIOR ANGLES
 The angles NOT between the parallel lines
 

 
 Angles A, D, F, and G are exterior angles.
 
 CORRESPONDING ANGLES
 Angles in the same place on each cross.
 

 
 ALTERNATE
 Means one angle on each side of the crossing line, so:
 
 ALTERNATE INTERIOR ANGLES
 

 
 ALTERNATE EXTERIOR ANGLES
 

 

   copyright 2005 Bruce Kirkpatrick

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