# 1.8 – Parallel Lines and Proofs

## Objectives

• Define skew and parallel lines.
• Use the correct notation to indicate parallel lines.
• Use the special angle relationships created by transversals and parallel lines to determine angle measures for corresponding angles, alternate interior angles, and consecutive angles.

## Key Terms

• Alternate Interior Angles – two angles formed by a line (called a transversal) that intersects two parallel lines. The angles are on opposite sides of the transversal and inside the parallel lines.
• Angle of Incidence – the angle between a ray of light meeting a surface and the line perpendicular to the surface at the point of contact.
• Angle of Reflection – the angle between a ray of light reflecting off a surface and the line perpendicular to the surface at the point of contact.
• Consecutive Interior Angles – two angles formed by a line (called a transversal) that intersects two parallel lines. The angles are on the same side of the transversal and are inside the parallel lines.
• Corresponding Angles – two nonadjacent angles formed on the same side (same place) of a line (called a transversal) that intersects two parallel lines, with one angle interior and one angle exterior to the lines.
• Intersect – to cross over one another.
• Law of Reflection – a law stating that the angle of incidence is congruent to the angle of reflection.
• Parallel Lines – lines lying in the same plane without intersecting. Two or more lines are parallel if they lie in the same plane and do not intersect. Notation: the symbol || means “parallel.” If parallel lines are graphed on a Cartesian coordinate system, they have the same slope.
• Skew Lines – lines that are not in the same plane. Skew lines do not intersect, and they are not parallel.
• Transversal – a line, ray, or segment that intersects two or more coplanar lines, rays, or segments at different points.

## Notes

Parallel Lines
• Two lines are parallel if they exist on the same plane and never intersect.
• If any two corresponding angels are congruent, then the lines are parallel.
• If any two alternate interior angles are congruent, then the lines are parallel.
• If any two consecutive interior angles are supplementary, then the lines are parallel.

Skew Lines
• One way that two lines won’t intersect is if they are not in the same plane.

Transversals
• When two lines are parallel, a transversal intersects both parallel lines, and two congruent angles are formed at the intersection.
• Conjecture: When a transversal intersects two parallel lines, it forms two congruent angles.
• Corresponding Angles Theorem
• When one transversal crosses a pair of parallel lines, it creates four pairs of corresponding angles.
• Corresponding angles are congruent.

• Alternate Interior Angles Theorem
• They are created by a transversal crossing parallel lines.