Vertical Angle

Date: 11/15/2001 at 14:52:10
From: Lyddie
Subject: Vertical Angles

I don't understand Vertical Angles! I believe that vertical angles are 
equal. Am I right? How can you tell if they are vertical angles?

Date: 11/15/2001 at 17:00:44
From: Doctor Peterson
Subject: Re: Vertical Angles

Hi, Lyddie.

Get a piece of paper, and draw an angle, which we'll call x:

                 /
                /
               /
              / x
             o----------

Now take a ruler and extend each ray on the other side of the angle:

                 /
                /
               /
              / x
   ----------o----------
          y /
           /
          /
         /

You've just made a new angle y. The angles x and y form a pair of 
VERTICAL angles; they are called that because they are on opposite 
sides of the same VERTEX. 

Think of the handle and blades of a very simple pair of scissors 
(with no bend to the handles) as another example. Notice that whatever 
angle you open the scissors to, the handles will be at the same angle, 
because vertical angles are always congruent.

The important thing to remember is that not all congruent angles are 
called "vertical"; angles are vertical because of where they are in a 
picture, not just because they happen to have the same measure. 
Whenever you see a pair of lines crossing, you will have two pairs of 
vertical angles: x and y, and p and q:

                 /
                /
               /
            p / x
   ----------o----------
          y / q
           /
          /
         /

Angles p and q are congruent, because they too are vertical angles.

Does that help?

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