Introduction:
This page was created to be an instructional guide on how to find certain angle measurements in specific geometric problems. I am constructing this tutorial page for the honorable Dr. Hellmers. Now I know that everyone out there is anxious to learn about how to find angle measurements, so lets begin with the tutorial.

In the picture on the left, line t intersects lines l and m. This is known as a transversal, because it intersects two or more lines in a plane at different points. The transversal forms 8 angles when it intersects lines l and m. Some of these angles form special relationships with each other. Exterior Angles Interior Angles Consecutive Interior Angles Alternate Interior Angles Alternate Exterior Angles Corresponding Angles Angle 1, Angle 2, Angle 7, Angle 8 Angle 3, Angle 4, Angle 5, Angle 6 Angles 3 and 5, Angles 4 and 6 Angles 3 and 6, Angles 4 and 5 Angles 1 and 8, Angles 2 and 7 Angles 1 and 5, Angles 2 and 6 Angles 3 and 7, Angles 4 and 8

Parallel Lines and Transversals: One of the first things you need to know about geometry is that the symbol || means that two lines are parallel. In the diagram on the right, the grey arrows represent that the lines are parallel. Therefore, Line BC is parallel to Line AD.

Angles and Parallel Lines: There are many relationships between angles and parallel lines. These relationships have been identified as postulates and theorums. Here are some postulates and theorums that will help in finding angels between parallel lines. Postulate 3-1 Corresponding Angles Postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. Theorem 3-1 Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. Theorem 3-2 Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary. Theorem 3-3 Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent. Theorem 3-4 Perpendicular Transversal Theorem In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. Example Problems More Example Problems