Vertical Angles
Vertical angles are angles that meet at exactly one point.  Here are some examples:
Theorem: vertical angles are congruent.  Here is how you can prove this theorem:

Given:  diagram as shown.

Prove:  angle AEB is congruent to
angle CED.

Statements                                         Reasons

1................................                       1. Given
2. Angle AEC is straight angle.             2. Assumed from diagram 
3.Angle AEB is supplementary             3. 2 angles that form a straight
to angle BEC. (see supplementary          line are supplementary.
angles for more information).
4.Angle DEB is a straight angle.           4. Same as step 2.
5. Angle DEC  is supplementary           5. Same as step 3.
to angle BEC.
6. Angle AEB is congruent to angle     6. Angles that are supplementary
GED.                                                 to the same angle are congruent.
                                                        (see supplementary angles for more
                                                          information).