Properties of Quadrilaterals & Geometric Terms

Vocabulary flashcards covering geometric quadrilaterals, their key properties, regional terminology differences, and basic area formulas based on the study guide.

Parallelogram

A quadrilateral in which opposite sides are parallel and congruent, opposite angles are congruent, consecutive angles are supplementary (add up to $180^\circ$), and diagonals bisect each other.

Rectangle

A parallelogram with four right angles ($90^\circ$) where opposite sides are equal and parallel, and diagonals are congruent and bisect each other.

Rhombus

A parallelogram with four sides of equal length (congruent), whose diagonals are perpendicular (intersect at $90^\circ$) and bisect opposite interior angles.

Square

A regular quadrilateral with four equal sides and four right angles ($90^\circ$) that inherits all properties of a parallelogram, rectangle, and rhombus; its diagonals are congruent, bisect each other, and intersect at right angles ($90^\circ$).

Kite

A quadrilateral with two distinct pairs of adjacent sides that are equal in length, one pair of congruent opposite angles (where unequal sides meet), and perpendicular diagonals where one diagonal bisects the other and bisects the interior angles at its endpoints.

Trapezoid / Trapezium (Properties)

A quadrilateral with at least one pair of parallel sides (called bases), where consecutive interior angles along the same leg are supplementary (add up to $180^\circ$).

Isosceles Trapezoid

A trapezoid whose non-parallel sides (legs) are congruent, base angles sharing the same base are congruent, and diagonals are equal in length (congruent).

Bisect each other

A condition where two lines or line segments divide each other into two equal parts at their point of intersection.

Consecutive Interior Angles

A pair of angles located on the same side of a transversal line and inside the two lines being crossed; when the lines are parallel, these angles are supplementary (add up to $180^\circ$).

Parallel Lines

Lines in the same plane that never intersect, maintaining a constant distance between them.

Perpendicular Lines

Two lines that intersect to form a right angle ($90^\circ$).

Supplementary

A term describing two angles whose sum is equal to $180^\circ$.

Trapezium (Regional Definitions)

A quadrilateral with no parallel sides according to US terminology, or a quadrilateral with exactly one pair of parallel sides according to UK terminology.

Trapezoid (Regional Definitions)

A quadrilateral with at least one pair of parallel sides according to US terminology, or no parallel sides according to UK terminology.

Congruent Non-Parallel Sides

The non-parallel legs of a trapezoid or trapezium that are equal in length, as found in an isosceles trapezoid.

Congruent

Having the exact same size and shape, where geometric figures are congruent if all corresponding sides and angles are equal.

Area of Parallelogram

The total surface space inside a parallelogram, calculated using the formula: $\text{Area} = \text{base} \times \text{height}$ ($A = b \times h$), where height is perpendicular to the base.

Area of Rectangle

The total surface space inside a rectangle, calculated using the formula: $\text{Area} = \text{length} \times \text{width}$ ($A = l \times w$).