Quadrilaterals can be arranged in a hierarchy based on their shared properties: square, rectangle, rhombus, parallelogram, trapezium, kite.
The relationship among the various quadrilaterals can be depicted as a hierarchy, where each type of quadrilateral inherits certain properties from its parent quadrilateral.
Square: A square is a special type of rectangle with all four sides congruent and all four angles right angles. It is the most specific quadrilateral, as it satisfies all the properties of a rectangle and additionally has congruent sides and right angles.
Rectangle: A rectangle is a parallelogram with all four angles right angles. It has two pairs of parallel sides and opposite sides congruent. Rectangles are more general than squares, as they only require right angles and not necessarily congruent sides.
Rhombus: A rhombus is a parallelogram with all four sides congruent. It is a special type of parallelogram where opposite sides are not only parallel but also congruent. Rhombuses have properties of both parallelograms and squares, having parallel sides and congruent opposite sides like parallelograms, and all sides congruent like squares.
Parallelogram: A parallelogram is a quadrilateral with two pairs of opposite sides parallel. It has opposite angles congruent and opposite sides congruent. Parallelograms are the most general type of quadrilateral in this hierarchy, as they only require parallel sides and do not impose any restrictions on angles or side lengths.
Trapezium: A trapezium is a quadrilateral with at least one pair of parallel sides. It does not have any specific requirements for angles or side lengths. Trapezoids are more general than parallelograms, as they only require one pair of parallel sides and not two.
Kite: A kite is a quadrilateral with two pairs of adjacent sides congruent. It has one pair of opposite sides congruent and one pair of opposite angles congruent. Kites are more specific than trapezoids, as they require two pairs of adjacent sides congruent and not just one pair of parallel sides.