Angles and Parallel Lines

In short: When a line crosses two parallel lines, it makes angles that follow three rules. Corresponding angles (an F shape) are equal, alternate angles (a Z shape) are equal, and co-interior angles (a C shape) add to $180^{\circ }$.

Before you start

• Parallel lines never meet. Diagrams show them with matching arrows.
• A line that cuts across two or more lines is called a transversal.
• Angles on a straight line add to $180^{\circ }$. Vertically opposite angles are equal (see Types of Angles).

Eight angles, four rules

When a transversal crosses two parallel lines, it makes 8 angles: 4 at each crossing.

Solving with the rules

Are the lines parallel?

You can use the rules backwards.

• If corresponding angles are equal, the lines are parallel.
• If alternate angles are equal, the lines are parallel.
• If co-interior angles add to $180^{\circ }$, the lines are parallel.

Quick summary

• A transversal crossing two parallel lines makes 8 angles with only 2 different sizes.
• Corresponding angles (F) are equal.
• Alternate angles (Z) are equal.
• Co-interior angles (C) add to $180^{\circ }$.
• Vertically opposite angles (X) are equal.
• Use the rules backwards to show lines are parallel.

Quiz