Quadrilaterals

Intuition and core definition

A quadrilateral is a simple polygon with four sides and interior-angle sum $360^\circ$. Common families form a hierarchy: parallelograms have two pairs of parallel sides; rectangles add right angles; rhombi add equal sides; squares satisfy both rectangle and rhombus definitions.

Notation, language, and conditions

A trapezoid is defined in some courses as having at least one parallel side pair and in others exactly one; state the convention. Kites have two distinct adjacent congruent side pairs under a common definition. Diagonal properties help classify: parallelogram diagonals bisect each other, rectangle diagonals are additionally congruent, rhombus diagonals additionally perpendicular.

Why this idea matters

Quadrilateral families form an inclusion hierarchy, so a figure may satisfy several names at once rather than belonging to only one box.

A dependable method

1. Mark parallel sides, equal sides, angles, and diagonal relationships from given evidence.
2. Use definitions before relying on appearance.
3. Move through the hierarchy from broad family to most specific justified class.
4. Use the $360^\circ$ angle sum for unknown measures.
5. Check each claimed class against every defining condition.

Worked example

Common mistakes