Geometry: Lines, Transversals, and Equations of Lines

Comprehensive vocabulary flashcards reviewing parallel and skew lines, transversals, angle relationships, angle theorems, and linear equations in coordinate geometry.

Parallel Lines

Coplanar lines that do not intersect.

Skew Lines

Non-coplanar lines that do not intersect and are not parallel.

Parallel Planes

Planes that do not intersect.

Perpendicular Lines

Lines that intersect to form right angles ($90^\circ$).

Transversal

A line that intersects two or more coplanar lines at distinct points.

Alternate Interior Angles

Nonadjacent interior angles that lie on opposite sides of the transversal.

Same-Side Interior Angles

Interior angles that lie on the same side of the transversal.

Corresponding Angles

Angles that lie on the same side of the transversal and in corresponding positions (the same relative spot at each intersection).

Alternate Exterior Angles

Nonadjacent exterior angles that lie on opposite sides of the transversal.

Same-Side Interior Angles Postulate

If a transversal intersects two parallel lines, then same-side interior angles are supplementary ($\text{sum} = 180^\circ$).

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternate interior angles are congruent.

Corresponding Angles Theorem

If a transversal intersects two parallel lines, then corresponding angles are congruent.

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then alternate exterior angles are congruent.

Slope ($m$)

The ratio of vertical change to horizontal change (rise over run, or change in $y$ divided by change in $x$), calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Positive Slope

The slope of a line that rises from left to right ($m > 0$).

Negative Slope

The slope of a line that falls from left to right ($m < 0$).

Zero Slope

The slope of a horizontal line ($m = 0$), where the change in $y$ is zero.

Undefined Slope

The slope of a vertical line, where the change in $x$ is zero ($\text{division by zero}$).

Slope-Intercept Form

The equation of a line written in the form $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept ($(0, b)$).

Point-Slope Form

The equation of a line written in the form $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a specific point on the line.

Standard Form of a Linear Equation

A linear equation written in the form $Ax + By = C$, where $A$, $B$, and $C$ are constants.

Horizontal Line Equation

A linear equation of the form $y = c$, representing a line that has a slope of $0$ and passes through points where the $y$-coordinate is always $c$.

Vertical Line Equation

A linear equation of the form $x = c$, representing a line that has an undefined slope and passes through points where the $x$-coordinate is always $c$.

Transitive Property of Congruence

A geometric property stating that if figure $A \cong B$ and figure $B \cong C$, then figure $A \cong C$.