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 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.