1. Polygon Hierarchy By: Madison Neal Polygons Quadrilaterals
Parallelograms
Trapezoids
Rectangles
Rhombus
Squares
By: Madison Neal

2. Why are polygons at the top of the Polygon Hierarchy?
Quadrilaterals
Parallelograms
Trapezoids
Rectangles
Rhombus
Squares
Why are polygons at the top of the Polygon Hierarchy?
What is a polygon? A polygon is any closed figure formed by segments that does not have any curved sides.
Squares, rhombuses, and rectangles are all formed by segments with no curved lines, and two sets of parallel lines, which would qualify them to be categorized as a parallelogram. In order for a shape to be a parallelogram, or a trapezoid, it has to be a quadrilateral, and all quadrilaterals are polygons, which automatically makes every shape listed a polygon.
Police Badge
This police badge is a real life example of a polygon because the figure is closed, it is formed by segments, and it does not have any curved sides.
Interesting fact: The word ‘polygon’ derives from the Greek word ‘poly’, meaning ‘many’ and ‘gonia’, meaning ‘angle.
Where did I find this picture?

3. Why are quadrilaterals beneath polygons in the polygon hierarchy?
Parallelograms
Trapezoids
Rectangles
Rhombus
Squares
Why are quadrilaterals beneath polygons in the polygon hierarchy?
What is a quadrilateral? A quadrilateral is any four-sided polygon whose angles have a sum of 360 degrees.
Squares, rectangles, rhombuses, and trapezoids are and will always be four sided shapes whose interior angles add up to 360 degrees. Being that a rectangles, a square, and a rhombus are all a parallelogram, that means a parallelogram is a quadrilaterals. Quadrilaterals are underneath polygons because not every polygon has four sides, but every quadrilateral will always be a polygon.
Notebook paper
This piece of notebook paper is a real life example of a quadrilateral because it a four-sided polygon, which is a closed figure with straight lines, and we can assume the angles add up to 360 degrees, making it a quadrilateral.
Interesting fact: The word ‘quadrilateral’ comes from ‘quad’ meaning ‘4’ and ‘lateral’ meaning ‘of sides’
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4. Why are parallelograms beneath quadrilaterals and polygons?
Trapezoids
Rectangles
Rhombus
Squares
Why are parallelograms beneath quadrilaterals and polygons?
What is a parallelogram? A quadrilateral with both pairs of opposite sides parallel.
All parallelograms have four sides and two sets of parallel lines, which means that all rectangles, rhombuses, and squares are parallelograms since they have four sides and two pairs of parallel lines. While a trapezoid does have four sides, it only have one set of parallel lines, which would explain why it is not connected to parallelograms on the polygon hierarchy. Since a trapezoid is a quadrilateral, that means that all quadrilaterals are not parallelograms which would explain why all quadrilaterals are not parallelograms. A simple explanation for why all polygons are not parallelograms is that a polygon does not have to have four sides, which explains why polygons are higher than parallelograms.
Chalk Board
This picture is a real life example of a parallelogram because it is four sided, and we can assume it is a rectangles, which has two sets of parallel sides, making it a parallelogram.
Where did I find this picture?

5. Polygons
Quadrilaterals
Parallelograms
Trapezoids
Rectangles
Rhombus
Squares
Why are trapezoids below polygons and quadrilaterals, but nothing is below trapezoids?
What is a trapezoid? A trapezoid is a quadrilateral with only one set of parallel sides.
A trapezoid is and will always be a quadrilateral, and since all quadrilaterals are polygons, that explain why trapezoids are beneath polygons, and quadrilaterals. Being that a trapezoid only has one set of parallel sides, it does not qualify to be a parallelogram, which explains why trapezoids are not connected to parallelograms or anything beneath it.
Guitar
This guitar represents a real life example of a trapezoid because it has four sides. And we can see that the top and the bottom are parallel to each other, which mean it qualifies to be a trapezoid.
Interesting fact: The altitude of a trapezoid is the perpendicular distance between the bases.
Where did I find this picture?

6. Polygons
Quadrilaterals
Parallelograms
Trapezoids
Rectangles
Rhombus
Squares
Why are rectangles below parallelograms and not connected to rhombuses?
What is a rectangle? A rectangle is a quadrilateral with four 90 degree angles, two sets of parallel lines, but all the sides are not the same length.
A rectangle has two sets of parallel lines, four sides, and it is a straight closed figure shape which explains why rectangles are always parallelograms, quadrilaterals, and polygons, and why parallelograms, quadrilaterals, and polygons are not always rectangles. Rectangles are not connected to trapezoids because a trapezoid has only one set of parallel lines, and a rectangle is not connected to rhombuses because the rectangle does not have all side lengths, and when a diagonal is placed through the rectangle it does not create two equal angle measures, while in a rhombus it does. A rectangle can not be classified as a square either because all of the rectangles sides are not congruent, which explains why squares are placed below rectangles, and not above them in the polygon hierarchy.
The American Flag
The American flag represents a life example of a rectangle because it is a quadrilateral, with four 90 degree angles, and two sets of parallel lines, but by the image you can see that the base and the side are not the same length. That would qualify this shape as a rectangle.
Where did I find this picture?

7. do
Polygons
Quadrilaterals
Parallelograms
Trapezoids
Rectangles
Rhombus
Squares
Why are rhombuses below parallelograms, above squares, and not connected to rectangles?
What is a rhombus? A rhombus is a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides
A rhombus is a parallelogram because it has two sets of parallel lines, and every parallelogram is a quadrilateral, which classifies every quadrilateral as a polygon. That explain why rhombuses are beneath parallelograms, quadrilaterals, and polygons. A rhombus can’t and will never be a trapezoid because a trapezoid is not a parallelogram and in order to be a rhombus, you have to be a parallelogram also. A rhombus is not a rectangle because a rectangle does not have all equal sides while rhombuses do. A rhombus is not a square because it does not have four right angles, but a square is a rhombus because a square is of all equal measures, as is the rhombus, which explains why a square is a rhombus, but a rhombus is not a square.
Folded Money
This folded money is a real world example of a rhombus because by eye you can see it is a parallelogram, and the sides do look to be equal. The angles are not 90 degrees, which could classify this shape as a rhombus.
Where did I find this picture?

8. Why are squares at the bottom of the polygon hierarchy?do
Polygons
Quadrilaterals
Parallelograms
Trapezoids
Rectangles
Rhombus
Squares
Why are squares at the bottom of the polygon hierarchy?
What is a square? A square is a quadrilateral with four equal straight sides and four right angles.
A square is a rectangle because a square has four right angles, and four equal sides, while a rectangle has only two equal sides, so a square is a rectangle but a rectangle isn’t a square. A square is also a rhombus because a rhombus has all equal sides, and the diagonal bisects the angles as it does for a square, but a rhombus is not a square because it does not have four right angles. Since a square is a rectangle, and a rhombus, and both of the two shapes are parallelograms, that means a square is also a parallelograms. All parallelograms are quadrilaterals, and polygons, which means all squares are also quadrilaterals and polygons. A square is not a rhombus and never will be because a rhombus does not have all equal sides, which a square does. There is nothing below squares because a rectangle, rhombus, nor a trapezoid will ever be a square. All quadrilaterals are not squares, for example, a trapezoid. And all polygons are not squares, for example, a triangle. That is why everything is above squares and nothing is below it.
Area Rug
This is a real life example of a square because this rug is a rectangle, and all rectangles are squares. It has four right angles, two pairs of parallel lines, and that makes it a rectangle, and a square.
Where did I find this picture?