When one line intersects a pair of lines (or more), we refer to it as a **transversal**.

**Transversal**

A line that intersects two or more lines in the same plane at different points.

When a transversal cuts through a pair of lines, it allows us to pair up and name the angles that are formed.

**Corresponding angles**

Angles that are in the same position on two lines in relation to a transversal.

**Same-side (consecutive) interior angles**

Angles that are on the interior of two lines on the same side of the transversal.

**Same-side (consecutive) exterior angles**

Angles that are on the exterior of two lines on the same side of the transversal.

**Alternate interior angles**

Angles that are on the interior of two lines on different lines and opposite sides of the transversal.

**Alternate exterior angles**

Angles that are on the exterior of two lines on different lines and opposite sides of the transversal.

### Exploration

Check the parallel lines box, then use the points to drag the transversal and the parallel lines.

What relationship do each of the types of angle pairs have?

Uncheck the parallel lines box and drag the lines. Are the relationships stated in the previous question still true? How do you know?

Check the parallel lines box again and drag one of the parallel lines to create a translation. How can you use a translation to verify the relationships you found?

**Parallel lines**

Two lines that never intersect. Lines are denoted as being parallel by the symbol \parallel.

When lines cut by the transversal are parallel, the angle pairs created have special relationships. They will either be **congruent** or **supplementary**.

**Corresponding angles theorem**

If a transversal intersects two parallel lines, then corresponding angles are congruent.

We can use our knowledge of translations to show this theorem is true. We can imagine translating one of the angles along the traversal until it meets the second parallel line. It will match the corresponding angle exactly.

The corresponding angles theorem can be used as a basis for proving relationships between other angle pairs, as given in the following theorems.

**Consecutive interior angles theorem**

If a transversal intersects two parallel lines, then same-side (consecutive) interior angles are supplementary.

**Consecutive exterior angles theorem**

If a transversal intersects two parallel lines, then same-side (consecutive) exterior angles are supplementary.

**Alternate interior angles theorem**

If a transversal intersects two parallel lines, then alternate interior angles are congruent.

**Alternate exterior angles theorem**

If a transversal intersects two parallel lines, then alternate exterior angles are congruent.