Parallel Lines and Transversals

When a line (called a transversal) crosses two parallel lines, it creates special angle relationships.

Key Vocabulary

• Parallel lines: Lines that never intersect (same direction)
• Transversal: A line that crosses two or more other lines

Angle Pairs Created

When a transversal crosses parallel lines:

Corresponding Angles

In the same position at each intersection. Rule: Corresponding angles are equal.

Alternate Interior Angles

On opposite sides of the transversal, between the parallel lines. Rule: Alternate interior angles are equal.

Alternate Exterior Angles

On opposite sides of the transversal, outside the parallel lines. Rule: Alternate exterior angles are equal.

Co-Interior Angles (Same-Side Interior)

On the same side of the transversal, between the parallel lines. Rule: Co-interior angles are supplementary (add to 180°).

Example Problem

If two parallel lines are cut by a transversal and one angle is 65°:

• Corresponding angle = 65°
• Alternate interior angle = 65°
• Co-interior angle = 180° - 65° = 115°

Why This Matters

These relationships help us:

• Prove lines are parallel
• Find unknown angles
• Solve real-world problems (architecture, design)