__Lines Cut by a Transversal__

A ** transversal**
is any line that cuts across two or more lines. For our study we have limited
the number to 2 lines. The transversal can form as many as 8 different angles
when cutting across two lines. In some cases, however, this number can be
limited depending on the way the cut is made and how many points of
intersection exist. For example, look at Figure 1:

**Figure 1**

Lines a, b, and c are all transversals because each of them
cuts two lines. Notice that each line forms 8 angles along its length over the
two lines that have been cut. What can you tell about these angles? What is the
relationship among them?

Look at line b as the
transversal and the eight angles it forms over lines a and
c. Pairs of corresponding angles would be: 5, 10; 8, 9; 6, 11;

7, 12. Pairs of alternate interior angles would be: 8, 11
and 7, 10; pairs of alternate exterior angles would be 5, 12 and 6, 9.

Question: Which angles in
the diagram must be congruent? Name the pairs in the same way as above. Why?

Now look at a set of lines a and b that are parallel and cut by
transversal line c. Again, the same types of angles form over the lines and the
transversal as above.

**Figure 2**

However, there is a new
relationship because we have parallel lines: the corresponding angles are
congruent with equal measures. This relationship also tells us that the
alternate interior and exterior angles are congruent because of the
corresponding angles and vertical angles in Figure 2. Can you find other interesting relationships,
such as angles that are not linear pairs that are supplementary?