Geometry: Lines, Angles, and Coordinate Geometry Review

Vocabulary practice flashcards covering parallel and skew lines, transversals, angle relationships, related postulates and theorems, triangle exterior angles, slope types, equations of lines, and parallelograms.

Parallel Lines

Coplanar lines that do not intersect.

Skew Lines

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

Parallel Planes

Planes that do not intersect.

Transversal

A line that intersects two or more coplanar lines.

Alternate Interior Angles

Non-adjacent interior angles that lie on opposite sides of the transversal between the two intersected lines.

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 relative to the lines.

Alternate Exterior Angles

Non-adjacent exterior angles that lie on opposite sides of the transversal.

Corresponding Angles Postulate

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

Alternate Interior Angles Theorem

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

Same-Side Interior Angles Theorem

If a transversal intersects two parallel lines, then the same-side interior angles are supplementary.

Alternate Exterior Angles Theorem

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

Converse of the Corresponding Angles Postulate

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.

Converse of the Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

Converse of the Same-Side Interior Angles Theorem

If two lines and a transversal form same-side interior angles that are supplementary, then the lines are parallel.

Converse of the Alternate Exterior Angles Theorem

If two lines and a transversal form alternate exterior angles that are congruent, then the lines are parallel.

Parallel Postulate

Through a point not on a line, there is one and only one line parallel to the given line.

Exterior Angle of a Polygon

An angle formed by one side of a polygon and the extension of an adjacent side.

Remote Interior Angles

The two non-adjacent interior angles inside a triangle relative to an exterior angle.

Triangle Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Slope ($m$)

The measure of the steepness of a line, defined as $m = \frac{\text{rise}}{\text{run}} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}$.

Slope-Intercept Form

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

Zero Slope

The slope of a horizontal line written in the form $y = \#$.

Undefined Slope

The slope of a vertical line written in the form $x = \#$, characterized by a zero in the denominator (e.g., $\frac{1}{0}$).

Parallel Lines Property of Vertical and Horizontal Lines

Any two vertical lines are parallel, and any two horizontal lines are parallel.

Perpendicular Lines Property of Vertical and Horizontal Lines

Vertical and horizontal lines are perpendicular to each other.

Parallelogram

A quadrilateral that has opposite sides that are parallel.