Chapter 3: Parallel and Perpendicular Lines

These flashcards cover critical concepts related to parallel and perpendicular lines, including their properties, theorems concerning angle relationships, slopes, equations, and distance calculations.

Transversal

A line that intersects two or more lines at different points.

Corresponding Angles Theorem

If a transversal intersects two parallel lines, each pair of corresponding angles is equal.

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, each pair of alternate interior angles is equal.

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, each pair of alternate exterior angles is equal.

Consecutive Interior Angles Theorem

If a transversal intersects two parallel lines, each pair of consecutive interior angles is supplementary.

Corresponding Angles Converse

If two lines are cut by a transversal and the corresponding angles are equal, the lines are parallel.

Alternate Interior Angles Converse

If two lines are cut by a transversal and the alternate interior angles are equal, the lines are parallel.

Alternate Exterior Angles Converse

If two lines are cut by a transversal and the alternate exterior angles are equal, the lines are parallel.

Consecutive Interior Angles Converse

If two lines are cut by a transversal and the consecutive interior angles are supplementary, the lines are parallel.

Slope of Parallel Lines

Parallel lines have the same slope.

Slope of Perpendicular Lines

Perpendicular lines have slopes that are opposite reciprocals of each other.

Point-Slope Form

An equation of a line in the form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Slope-Intercept Form

An equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.

Distance Between a Point and a Line

The shortest distance from a point to a line is measured along a perpendicular line.

Distance Formula

The formula used to determine the distance between two points in a coordinate plane, given by d = √((x2 - x1)² + (y2 - y1)²).

Finding Area of Triangle/Parallelogram

The area can be determined using the height, which is related to the distance between a point and a line or the distance between two parallel lines.