Geometry: Parallel and Perpendicular Lines, Angle Relationships, and Proofs

Vocabulary flashcards reviewing lines and planes in space, transversal angle pairs, slope and linear equations, and parallel line theorems from high school geometry.

Skew Lines

Lines in three-dimensional space that do not intersect and are not coplanar, such as lines (\overleftrightarrow{CG}) or (\overleftrightarrow{BF}) relative to (\overleftrightarrow{AD}) in a rectangular prism.

Parallel Lines

Coplanar lines that never intersect and maintain the same distance apart, having equal slopes.

Perpendicular Lines

Lines that intersect to form right angles ($90^\circ$), having slopes that are negative reciprocals of one another.

Parallel Planes

Planes in space that do not intersect, named by at least three non-collinear points (for example, plane $BFCG$ is parallel to plane $ADE$).

Transversal

A line that intersects two or more coplanar lines at distinct points, creating angle pairs such as interior, exterior, corresponding, and alternate angles.

Alternate Interior Angles (AIA)

A pair of angles that lie on opposite sides of the transversal on the interior of the two intersected lines (e.g., $\angle 6$ and $\angle 15$).

Alternate Exterior Angles (AEA)

A pair of angles that lie on opposite sides of the transversal on the exterior of the two intersected lines (e.g., $\angle 1$ and $\angle 8$).

Consecutive Interior Angles (CIA)

A pair of interior angles located on the same side of the transversal (e.g., $\angle 3$ and $\angle 11$), which are supplementary when the lines are parallel.

Corresponding Angles (CA)

A pair of nonadjacent angles that occupy matching relative positions at each intersection formed by a transversal (e.g., $\angle 5$ and $\angle 13$).

Slope Formula

The formula used to determine the rate of change or steepness of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$, defined as $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Slope-Intercept Form

The linear equation form $y = mx + b$, where $m$ represents the slope and $b$ represents the $y$-intercept of the line.

Parallel Lines Slope Property

The geometric principle establishing that two non-vertical lines are parallel if and only if they possess identical (the same) slopes.

Perpendicular Lines Slope Property

The geometric principle establishing that two non-vertical lines are perpendicular if and only if their slopes are negative reciprocals (e.g., $m = 4$ and $m_{\perp} = -\frac{1}{4}$).

Supplementary Angles

Two angles whose degree measures add up to exactly $180^\circ$.

Alternate Interior Angles Theorem

A theorem stating that if two parallel lines are cut by a transversal, then the resulting pairs of alternate interior angles are congruent ($\angle 1 \cong \angle 3$).