■ Quadrilaterals and Polygons

Quadrilateral Hierarchy

All squares are rectangles; all rectangles are parallelograms; all parallelograms are quadrilaterals. The hierarchy from most specific to most general: Square → Rectangle → Parallelogram → Quadrilateral.

Key Properties

• Parallelogram: opposite sides parallel and equal; opposite angles equal; diagonals bisect each other
• Rectangle: parallelogram + four right angles; diagonals equal length
• Rhombus: parallelogram + four equal sides; diagonals perpendicular bisectors
• Square: rectangle + rhombus
• Trapezoid: exactly one pair of parallel sides (bases)

Polygon Angle Formulas

Interior angle sum: (n − 2) × 180°

Each interior angle (regular polygon): (n − 2) × 180° / n

Exterior angle sum: always 360° for any convex polygon

Each exterior angle (regular polygon): 360° / n