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Let me introduce you to the quadrilateral family. A four sided family that lives on Polygon Street.
There are three main members to this family, kite, trapezoid, and parallelogram. Like any family they look and act similarly, but are also very different. Kite had two consecutive pairs of sides the same, but her opposite sides were different. Her diagonals were also unequal. She loved to cover herself in cloth, and go fly high in the sky.
Trapezoid had exactly one pair of parallel sides, and nice supplementary legs. Although trapezoid was friendly, friends and family could never figure out exactly what defined her. 
Parallelogram, with her two sets of parallel sides was very popular, and was the first family member to marry. She had two small shapes, rhombus and rectangle.
Rectangle was very much like his mother shape, two parallel sides, and four 90 degree angles. Rhombus was great son with equal sides, two pairs of parallel sides, and equal opposite angles. Mom was proud of the beautiful shapes of her two children.
One day rectangle and rhombus told mom they wanted a new pet shape. Rectangle wanted a three sided pet, rhombus wanted a five sided pet shape. Mom said “I know what to do, I will be right back." When she returned she had the new pet shape. “meet square” she said. "He is perfect, two parallel sides, equal sides, and four 90 degree angles." Rhombus and Rectangle loved their new pet shape.
a rhombus/ 4 sided polygon
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  Kite
• A Quadrilateral that has two consecutive pairs of congruent sides
But opposite sides are not congruent
• Diagonals are not congruent
• One pair of opposite angles that are congruent
• The other pair of opposite angles are bisected by one of the diagonals
• Diagonals are not congruent


Parallelogram
• A quadrilateral with both pairs of sides parallel
•Opposite angles and sides are congruent
•Consecutive angles are supplementary
•Diagonals Bisect one another

​ Trapezoid
•A quadrilateral with exactly one pair of opposite sides parallel
•Leg angles are supplementary


Rhombus
•A parallelogram with four congruent sides
•Diagonals are perpendicular and bisect a pair of opposite angles
•Diagonals are not congruent

  Isosceles Trapezoid
• A trapezoid whose legs are congruent
• Both pairs of base angles are congruent
• Diagonals are congruent

Rectangle
• A parallelogram with four congruent 90 degree angles
• Diagonals are congruent
• Diagonals create four isosceles triangles

                  Square
• A parallelogram with four congruent angles and sides
• Diagonals are congruent
• Has all the properties of a rhombus and a rectangle


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The Quadrilateral Family Tree

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Area formulas
Perimeter formulas plane shapes
Parallelogram
Kite
Trapezoid
Square
Rhombus
Rectangle

Four Sided Polygon

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The Quadrilateral Family Tree

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kite quadrilateral member quadrilateral family
a rhombus/ 4 sided polygon
parallelogram a member of the quadrilateral family
rectangle 4 sided polygon
parallelogram a member of the quadrilateral family
square a quadrilateral
quadrilateral is a polygon with four sides. There are 4 major types of quadrilaterals, kites, parallelogram, trapezoids, and then quadrilaterals that do not fit into any of these groups.  Parallelograms have several subgroups including rhombi, rectangles and squares. Below is a diagram of the groups and further below are videos with explanations of the properties unique to each one.
Common Core Standard  7.G.6

The Quadrilateral Family Tree Story