Parallel lines are lines that never intersect (cross each other), no matter how far they extend. In other words, the distance between the two lines remains constant at every point along their lengths. When represented in a coordinate plane, parallel lines have the same slope.
A transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects parallel lines, it forms pairs of angles with important properties.
Alternate angles are formed on opposite sides of the transversal, and between the parallel lines. When two lines are parallel, their alternate angles are equal.
Corresponding angles are angles that have the same position when two parallel lines are crossed by another line called a transversal. They are created where the transversal intersects each parallel line.
When lines are parallel, their corresponding angles are equal.
Co-interior angles are formed on the same side of the transversal and between the parallel lines. When lines are parallel, the sum of the interior angles on the same side of the transversal is 180°.
We’ve already looked at alternate angles, corresponding angles, and co-interior angles individually. Now, let’s look at how they all work together.
In the diagram below, two parallel lines are intersected by a transversal, creating a variety of angles.
Notice how the angles are either equal or add up to 180° based on their position and relationship to the transversal and parallel lines.