A quadrilateral hierarchy, also known as a ‘family tree‘, is a graphical way of representing the different types of quadrilaterals (members), based on their relationships.

How to Make a Hierarchy

Concept: By going through the definition and properties of each special quadrilaterals, we find most of them to share some common characteristics with some other quadrilaterals. This type of overlapping relationship between the different types of quadrilaterals is shown below using a quadrilateral family tree.

Explanation: As shown above, all quadrilaterals can be divided into three types; a parallelogram, a trapezoid, and a kite, based on the presence and number of parallel sides. A parallelogram has two pairs of parallel sides, a trapezoid, on the other hand, has only two parallel sides, while a kite has no parallel sides at all.

Again, a parallelogram can have all its four sides equal to become a rhombus or its four angles equal to become a rectangle, which is thus placed below the parallelogram. Interestingly a square which is placed below the rectangle and a rhombus is found to share both their properties of having all sides equal and all angles equal.

This same concept is used in case of trapezoid where an isosceles trapezoid is a special case of a trapezoid having two equal sides, while a rhombus is a special case of a kite when all its sides are equal.

Quadrilateral Flow Chart Based on Hierarchy

Another way of representing the quadrilaterals, based on the quadrilateral hierarchy is by using a flow chart.

The above flowchart shows a step by step representation of different quadrilaterals with their properties and their relationship to one another.

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