Polygons and Quadrilaterals

Vocabulary flashcards covering the definitions, angle sum formulas, and classification properties of polygons and quadrilaterals.

Polygon

A closed figure formed by three or more line segments, called sides.

Interior Angle Sum Formula

The formula $S = (n - 2)180^\circ$, where $n$ represents the number of sides of a polygon, used to calculate the sum of its interior angles.

Regular Polygon

A polygon with all sides congruent ($\cong$) and all angles congruent ($\cong$).

Interior Angle Measure of a Regular Polygon

The measure of a single interior angle found by dividing the sum of the interior angle measures by the number of sides: $\frac{(n - 2)180^\circ}{n}$.

Exterior Angle of a Polygon

An angle formed outside a polygon that is supplementary to its adjacent interior angle.

Sum of the Exterior Angle Measures

The sum of the measures of the exterior angles of any convex polygon, which will always equal $360^\circ$.

Exterior Angle Measure of a Regular Polygon

The measure of each exterior angle in a regular polygon, determined by dividing $360^\circ$ by the number of sides: $\frac{360^\circ}{n}$.

Number of Sides ($n$) Formula

The formula $n = \frac{360^\circ}{\text{Exterior Angle}}$, used to find the number of sides of a regular polygon when an exterior angle measure is given.

Kite

A quadrilateral with exactly two pairs of consecutive congruent sides, one pair of congruent opposite angles, and diagonals that are perpendicular.

Trapezoid

A quadrilateral with only one pair of opposite sides parallel (called bases) and consecutive angles between the bases that are supplementary.

Midsegment of a Trapezoid

A line segment that connects the midpoints of the legs of a trapezoid and has a length equal to the average of the two bases.

Isosceles Trapezoid

A trapezoid whose non-parallel sides (legs) are congruent, diagonals are congruent, base angles are congruent, and opposite angles are supplementary.

Parallelogram

A quadrilateral with two pairs of parallel sides, opposite sides congruent, opposite angles congruent, consecutive angles supplementary, and diagonals that bisect each other.

Consecutive Angles of a Parallelogram

Angles that lie along the same consecutive side of a parallelogram and are supplementary (sum to $180^\circ$).

Diagonals of a Parallelogram

Line segments joining opposite vertices of a parallelogram that bisect each other.

Rectangle

A parallelogram with four right angles ($90^\circ$) and congruent diagonals, retaining all standard properties of parallelograms.

Diagonals of a Rectangle

Segments connecting opposite corners of a rectangle that bisect each other and are congruent ($\cong$).

Rhombus

A parallelogram featuring four congruent sides, perpendicular diagonals, and diagonals that bisect opposite angles.

Diagonals of a Rhombus

Segments connecting opposite vertices of a rhombus that intersect at right angles ($\perp$) and bisect opposite angles.

Square

A quadrilateral having all properties of a parallelogram, rectangle, and rhombus (four right angles, four congruent sides, and diagonals that are congruent, perpendicular, and bisect opposite angles).