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Geometry › Quadrilaterals
Quadrilaterals
Four sides, four corners — and a family tree of overlapping definitions. A square is a rectangle is a rhombus is a parallelogram.
Quadrilateral family
Selected
Square
Four equal sides, four right angles.
- 4 equal sides
- 4 right angles
- Diagonals equal & perpendicular
Every interior angle sum = 360°
The family tree
- Square — 4 equal sides, 4 right angles. Most special.
- Rectangle — 4 right angles, opposite sides equal.
- Rhombus — 4 equal sides, opposite angles equal.
- Parallelogram — both pairs of opposite sides parallel and equal.
- Trapezoid (US) / trapezium (UK) — at least one pair of parallel sides.
- Kite — two pairs of adjacent equal sides.
Inheritance
A square inherits all the properties of its ancestors: it's a rectangle, a rhombus, a parallelogram, and a kite — all at once. The names overlap on purpose.
Always-true facts
- The four interior angles always sum to 360°.
- The diagonals of a parallelogram bisect each other.
- The diagonals of a rhombus are perpendicular.
- The diagonals of a rectangle are equal in length.
Area formulas
- Square:
A = s² - Rectangle:
A = w × h - Parallelogram:
A = base × height - Rhombus:
A = ½ × d₁ × d₂(diagonals) - Trapezoid:
A = ½(a + b) × h - Kite:
A = ½ × d₁ × d₂