Parallel Lines Cut By A Transversal

A transversal is a line that crosses (intersects) two or more lines at different points. When this happens, it creates several important angle relationships that follow specific rules.

When you're working with parallel lines cut by a transversal, look for these key angle pairs:

• Corresponding angles are angles in the same position on different lines (like both in the top right corner) and are equal when lines are parallel
• Alternate interior angles are inside the parallel lines but on opposite sides of the transversal - these are always equal
• Alternate exterior angles are outside the parallel lines but on opposite sides of the transversal - also always equal

The relationship between angles doesn't stop there. Vertical angles are formed when lines cross and are always equal, while supplementary angles add up to 180°. Consecutive interior angles (sometimes called same-side interior angles) lie on the same side of the transversal between the lines and add up to 180° when the lines are parallel.

Pro Tip: Remember this shortcut - if two parallel lines are cut by a transversal, corresponding angles are equal (≅), alternate angles are equal (≅), and consecutive interior angles are supplementary $sum = 180°$.