Transversals and Related Angles

For two or more lines, a transversal is any line which intersects two lines at distinct points. In the following figure, L₁ and L₂ are two lines which are cut at A and B by a transversal L₀, resulting in a number of angles being formed:

There is a specific terminology associated with the angles formed when a transversal cuts two lines, as shown above. Let us quickly go over that terminology by taking the example of the figure above:

Corresponding angles

The following pairs of angles are corresponding angles:

• \(\angle 1\) and \(\angle 5\)
• \(\angle 2\) and \(\angle 6\)
• \(\angle 3\) and \(\angle 7\)
• \(\angle4\) and \(\angle 8\)

Alternate interior angles

The following pairs of angles are alternate interior angles:

• \(\angle 3\) and \(\angle 5\)
• \(\angle4\) and \(\angle 6\)

Alternate exterior angles

The following pairs of angles are alternate exterior angles:

• \(\angle 1\) and \(\angle 7\)
• \(\angle 2\) and \(\angle 8\)

Co-interior angles

The following pairs of angles are co-interior angles:

• \(\angle 3\) and \(\angle 6\)
• \(\angle4\) and \(\angle 5\)

We will now go on to the specific case of two parallel lines being cut by a transversal.