Alternate Exterior Angles

Date: 06/03/2002 at 15:45:58
From: S.B.
Subject: Geometry definitions

Dear Dr. Math

I have been trying to find out what exterior alternate angles are 
for hours! My teacher assigned us a vocabulary sheet for geometry, and 
the only term I can't find is alternate exterior angles. I know what 
an alternate interior angle is, but not an exterior one. I am 
completly clueless! Please help, A.S.A.P.!

Thanks------ S.B.

Date: 06/03/2002 at 17:08:38
From: Doctor Peterson
Subject: Re: Geometry definitions

Hi, S.B.

Here's a clue, from everyday English usage: "interior" means 
"inside", and "exterior" means "outside". (You may see those words on 
paint can labels, for example.)

So alternate _interior_ angles are on opposite sides of the 
transversal, _between_ the parallel lines, like the pair of x's and 
the pair of y's here:

      \
    ---+-------
      x \y
         \
         y\ x
    -------+---
            \

Alternate _exterior_ angles are also on opposite sides of the 
transversal, but _outside_ the parallel lines:

     x\ y
    ---+-------
        \
         \
          \
    -------+---
          y \x

I suspect a lot of students hear these phrases as a whole, and never 
stop to think what the individual parts (alternate, interior, 
exterior) mean -- because they expect math terms to be 
incomprehensible and unrelated to real life! Sometimes math makes 
more sense than you realize at first.

Maybe I can also help you not have to look for hours next time. To 
find what a word means, I would first go to a regular English 
dictionary; then maybe try one of the dictionary or encyclopedia 
resources listed in our FAQ, or search our site; then go to 
google.com and enter the phrase "alternate exterior angles" to see if 
there is a definition on the web. You'll find it!

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/