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A Quadrilateral Story

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Liem Budzien

on 11 April 2014

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Transcript of A Quadrilateral Story

In a distant galaxy across the universe, there was a solar system called the Quadrilateral System. Every living thing inside the Quadrilateral System had four sides, no more, no less. This system resided in the Polygon galaxy in which every type of polygon resided. Within the Quadrilateral System, there were three main groups of planets. There was the trapezoid cluster, which was on the inside of the asteroid belt. On the other side of the asteroid belt lay the parallelogram cluster, which contained the Rhombus, Squares and Rectangles planets. Lastly is the planet kite, sitting out far away from the sun, isolated from all the other planets, kind of like Pluto in our solar system. All of these clusters contained quadrilaterals, but each had slightly different characteristics and special properties.
In A Land Far Far Away...
The rhombus live on a planet in the parallelogram cluster of the Quadrilateral System. Every rhombus has four congruent sides. Also, the diagonals of a rhombus bisect each other, forming 90 degree angles at the intersection. The rhombus consider themselves to be equal at all times and never unfair or unjust.
The Rectangles live on the planet next to the rhombus. In order to be a rectangle, have have to have four 90 degree angles. As a rectangle, your diagonals bisect each other, but are not perpendicular. They are also congruent. The rectangles aren't always fair. Sometimes they give some sides more than others.
By Liem Budzien
A Quadrilateral Story
Squares are descendants of the Rectangles and the Rhombus. They have four congruent sides like a rhombus and diagonals that bisect and are perpendicular, but also has the properties of rectangles such as having congruent diagonals and 90 degree angles. Squares consider themselves to be the most elite out of all the parallelograms because they contain the special properties of the rectangles and rhombus.
The trapezoids were considered inferior as their bases were different lengths. However, their bases are parallel to each other. One special character of trapezoids is that their median equals 1/2 of the two bases added up. Any trapezoid can look vastly different, from having two right angles to having all different angles.
Isosceles Trapezoids
Isosceles trapezoids dwell on one of the moons orbiting the planet normal trapezoids live on. The isosceles trapezoids are considered to be better looking then normal trapezoids, as their legs are the same length along with having two pairs of congruent angles on the top and bottom of the trapezoid. However, the isosceles trapezoids still suffer from having their bases being different lengths.
Family Tree
The kites are descendents of the quadrilaterals and isosceles triangles. The kites have four sides like a normal quadrilateral, but have two pairs of consecutive congruent angles, with the two pairs being different lengths than each other. In a kite, opposite angles are congruent and the diagonals intersect perpendicularly, forming two pairs of congruent triangles inside of the kite. The diagonals also bisect the vertices they begin and end in.
Thank you for your time. I hope you have learned more about quadrilaterals from this presentation.
In the parallelogram cluster, each and every quadrilateral had two pairs of opposite and congruent sides and angles. Hence the name, both pairs of the opposite sides are parallel. In a parallelogram, all consecutive sides are also supplementary. The parallelogram cluster used to be united, but broke away as the squares, rhombus and rectangles only saw the differences between them and ignored the similarities. Some parallelograms did not fit into the rhombus, square or rectangle categories, so they lived as outcasts because they did not have any extra special properties like rhombus or rectangles.
Parallelogram Cluster
Isosceles Trapezoid
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