One pair of parallel sides

Trapezium

Two pairs Two pairs of equal of equal parallel adjacent sides sides

Kite

Four sides equal Four right angles

Rhombus

Four right angles Four equal sides

Square

Legend Quadrilaterals A, B, C, D are angles a, b, c, d are side lengths B All sides in one plane Not all sides in one plane b Skew a C Planar c A D No crossed sides d Two crossed Note that all properties are sides Simple inherited along the arrows

All angles < 180° Complex One angle > 180° Arrow Antiparallelogram (Self-intersecting) Concave (aka Dart/Chevron) Convex

Two pairs of Two pairs of opposite equal adjacent equal sides sides

Opposite angles sum to 180° Opposite side One pair Equal One pair lengths have Perpendicular of parallel diagonals of opposite equal sums diagonals sides equal sides Tangential Watt Cyclic Ex-tangential Orthodiagonal A + C = B + D = 180° (Inscriptible) a + c = b + d 2 2 2 2 Trapezium Equidiagonal a + c = b + d a + c = b + d A + B = C + D = 180°

One pair of Opposite side lengths parallel ides Non-equal Two pairs of equal have equal sums opposite adjacent sides sides parallel Two One pair of Non-parallel Two pairs A second adjacent parallel sides Opposite of equal sides equal (if r=∞) pair of parallel right sides Opposite adjacent sides angles equal sum angles sides equal sum Right-angled Isosceles Tangential Parallelogram Bicentric (‘Rhomboid’ if adjacent trapezium trapezium sides are unequal) trapezium

Two Four sides Four Four sides Four right Four Four right One pair of opposite equal sides equal angles right angles opposite right equal angles equal sides angles Opposite side Third lengths have equal sums side equal Four right angles Right kite Quadric Rectangle 3-sides-equal Isosceles (‘Oblong’ if adjacent trapezium tangential sides are unequal)

Four right angles Four Four equal equal sides Four right angles sides Four equal sides

Square Equilic

60°