Parallel Lines Cut by a Transversal

When a line (called a transversal) crosses two parallel lines, it creates eight angles with special relationships. Think of these angle pairs as your geometry toolkit!

Adjacent angles form a straight line and are supplementary, meaning they add up to 180°. For example, ∠1 + ∠2 = 180° and ∠5 + ∠7 = 180°. These angle pairs sit next to each other along the transversal.

Vertical angles are always equal in measure and form an X-pattern. When two lines intersect, the angles opposite each other are equal. Examples include ∠1 = ∠3 and ∠2 = ∠4.

📐 Angle Tip: When you identify one angle in a parallel line system, you can find all the others! This is why these relationships are so powerful in geometry proofs.

Corresponding angles are in the same position relative to both parallel lines and the transversal. These angles are always equal - like ∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8. They "correspond" because they appear in the same spot on each line.

Alternate interior angles are on opposite sides of the transversal but inside the parallel lines. These angles are equal, such as ∠3 = ∠6 and ∠4 = ∠5. Alternate exterior angles work the same way but outside the parallel lines, like ∠1 = ∠8 and ∠2 = ∠7.

Consecutive interior angles $sometimes called same-side interior angles$ are on the same side of the transversal and inside the parallel lines. These angle pairs are supplementary, meaning ∠3 + ∠5 = 180° and ∠4 + ∠6 = 180°.