Chapter Summary 03 Parallel and Perpendicular Lines

Parallel Lines

Two lines that do not intersect and are coplanar.

Skew Lines

Lines that do not intersect and are not coplanar.

Parallel Planes

Two planes that do not intersect.

Corresponding Angles

Angles that have corresponding positions when two lines are cut by a transversal.

Alternate Interior Angles

Angles that lie between two lines and on opposite sides of a transversal.

Alternate Exterior Angles

Angles that lie outside two lines and on opposite sides of a transversal.

Consecutive Interior Angles

Angles that lie between two lines and on the same side of a transversal.

Slope

The ratio of the rise (change in y) to the run (change in x) of a line.

Slope-Intercept Form

A linear equation written in the form y = mx + b, where m is the slope and b is the y-intercept.

Point-Slope Form

A linear equation written in the form y - y₁ = m(x - x₁), indicating the line passes through the point (x₁, y₁) with slope m.

Slopes of Parallel Lines

Two distinct non-vertical lines are parallel if and only if they have the same slope.

Slopes of Perpendicular Lines

Two non-vertical lines are perpendicular if and only if the product of their slopes is -1.

Distance from a Point to a Line

The length of the perpendicular segment from the point to the line; the shortest distance between the point and the line.