Vertical Angles

Date: 10/27/96 at 19:24:46
From: Kimberly
Subject: Geometry

Exactly what are vertical angles?  

Thanks,
Kimberly

Date: 10/28/96 at 12:14:43
From: Doctor Mike
Subject: Re: Geometry

Hi Kimberly,
  
Vertical angles are like a pair of scissors -- you can't have just one 
scissor, and you can't have just one vertical angle.  If you draw two 
straight lines that intersect then 4 angles are formed. Example: 
  
                       \   
                        \
                         \
                          \  A
      _____________________\_______________________
                            \
                          A  \   
                              \  
                               \  
  
The pair of angles marked "A" are vertical angles.  The other 2 angles
are also a pair of vertical angles.  You probably have heard the 
theorem that "vertical angles are equal".  That is what lets me label 
those two angles with the same letter name "A".  If one is 123 
degrees, then so is the other.
  
Vertical angles are like a pair of scissors in another way.  If you
open the scissors and lay them on a table, it looks sort of like two
lines intersecting at the point where the two parts of the scissors 
are attached. 
  
I'm not sure why the word "vertical" is used for such angles.  It
probably does not have anything to do with vertical in the sense of
straight up and down. Since the point where the lines meet can be
called a vertex, the word vertical could be used to mean opposite
angles that meet at the vertex.  
  
Are you interested in foreign languages?  Lots of mathematicians are.
That is because mathematicians from foreign countries write 
interesting mathematical books and magazine articles in their own 
language.  In order to read that stuff before it gets translated, you 
have to know something about the other languages.  I happen to know a 
little German so I looked up some geometry words in that language. 
"Winkel" is angle. "Punkt" is point.  "Scheitelpunkt" is the point 
where lines cross over. "Scheitelwinkel" means vertical angle. 
"Scheitel" by itself means the top or summit, like of a mountain.  If 
you look at the outline of a mountain from far away it looks like two 
lines meeting at the top. 
  
I hope this helps. If you get in a jam again, write us again.  

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/