Vertical angles

Date: Tue, 15 Nov 1994 17:16:33 -0500 (EST)
From: Anonymous
Subject: QUESTION

Dr. Math,

        Here is a question for you. Are vertical angles congruent in
Euclidean geometry?

Date: Tue, 15 Nov 1994 19:25:59 -0500 (EST)
From: Dr. Ken
Subject: Re: QUESTION

Hello there!

Boy, am I excited to answer your question!  And I sound a resounding 
"YES!!"  Vertical angles ARE congruent in Euclidean Geometry!! 

Do you see why this is true?  I'll give you a hint:  If you have a pair of
vertical angles A and C, like this:

                            |       /
                            |      /
                            |     /
                            |    /
                            | A /
                            |  /
                            | /
                            |/
                            |
                           /|  B
                          / |
                         /  |
                        / C |
                       /    |
                      /     |
                     /      |

If the measure of angle A is x degrees, what is the measure of angle B?
Then using the measure of angle B, what is the measure of angle C?

It is a quite interesting fact that vertical angles in ANY (holy cow!)
geometry are congruent.  The proof is a little deeper, and since I don't
have my Non-Euclidean Geometry book handy, I'll not give it to you right
now, because I'd probably mess up.  But if you're interested, let us know
and I'll try to dig it up.  

I hope this helps!

-Ken "Dr." Math