The Parallelogram's Dilemma

By Author Name

Coach Grumpylateral

Once upon a time, in an alternate town called Geoville, where quadrilaterals once competed for sports glory, there was a notoriously rigid and grumpy quadrilateral coach. This coach, known for his stern nature, had a simple and exclusive rule for all his players: each shape could participate in a sport only if the sport needed its shape.

For example, a tennis court had no need for a trapezoid (as trapezoids had only one set of parallel lines), so the poor but well-meaning Trapezoid Tony could not play tennis because a tennis court does not have any trapezoid shapes.

No trapezoids needed here.

No trapezoids needed here.

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Blair the Square

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Coach Grumpylateral's favorite and star athlete, known to all his friends as Blair the Square, found his calling in the boxing ring. He had a muscular frame with his equal sides and equal angles and the symmetry of his structure made him an unbeatable champion, a force to be feared - every bit as square as the ring he dominated.

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Parallela

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Meanwhile, Parallela was coach Grumpylateral's least favorite and most ignored athlete. She didn't seem to fit in anywhere. Sure, she had two sets of parallel sides, her two opposite sides were congruent, and her opposite angles had equal measures, just like Blair the Square. Then why did coach hate Parallela so much? The problem for coach was that Parallela did not have any right angles and her adjacent sides were unequal in length.



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The Misfit

Coach did not know of any sports that used parallelograms like Parallela, nor any that even wanted to. Parallela was always left out of all the games her friends played and this feeling became unbearable when the mean coach decided to give all unwanted shapes a final warning: if Parallela did not find a sport that needed her shape by the end of the day, she would be banished from Geoville forever.
Day turned into evening as Parallela, now under the pressure of the looming deadline, began her desperate search.
Even the most disliked and annoying student in Geoville, Pompous Rhombus, had found his calling playing second base on the baseball infield - shaped like a perfect rhombus.
Hope was dwindling, and all her geometric friends worried about her. She wondered why she just couldn't be like her best friend Mangle.

Mangle the Rectangle

Mangle was not a good athlete. In fact, he would much rather be playing his piano with his rectangle friends, but he was a sweet guy and everybody liked him. He never wanted to be an athlete but because he had such a common shape in sports - with his four right angles and unequal adjacent sides - Coach Grumpylateral demanded that Mangle play almost every single sport.

First, there was tennis. The rectangle of the court was divided into two perfect rectangles for doubles. Mangle moved with ease through the lines of the service boxes and the baselines.

Next, he was called on to play soccer. He did enjoy being outside in the sun and on the grass of the rectangular field, with its goal and penalty areas, having unequal adjacent sides - just like his own.

Mangle Just Needs a Break

Trapezoid Tony

When Mangle heard about the struggles of his friend Parallela, he thought of every sport he had ever played but but could not come up with any that needed a parallelogram shaped like Parallela. He did however, find a sport for their common friend, Trapezoid Tony. During his trip to Geoeurope, Mangle noticed that the hockey ring uses an unusual quadrilateral shape with one, and only one pair of parallel lines. It was a trapezoid. When Trapezoid Tony heard about this he was jumping with joy - Tony, like Parallela, thought he would never fit in anywhere. Tony grew to become the most intimidating goalie anybody would ever see on a hockey ring.

Once, when Mangle finally thought he could take a break on a family trip to Geoeurope, he realized that he was adept at playing sports he had never even heard of: the Frenchilateral children wanted Mangle to play rugby with them; the Britishlateral students begged him to play on the pitch of the cricket field - whatever that meant?

Trapezoid Tony

When Mangle heard about the struggles of his friend Parallela, he thought of every sport he had ever played but but could not come up with any that needed a parallelogram shaped like Parallela. He did however, find a sport for their common friend, Trapezoid Tony. During his trip to Geoeurope, Mangle noticed that the hockey ring uses an unusual quadrilateral shape with one, and only one pair of parallel lines. It was a trapezoid. When Trapezoid Tony heard about this he was jumping with joy - Tony, like Parallela, thought he would never fit in anywhere. Tony grew to become the most intimidating goalie anybody would ever see on a hockey ring.

Dwight

Of all the shapes remaining in Geoville without a sport to play, this left just Parallela and Dwight. Dwight was a kite with two pairs of adjacent that were equal, but his opposite sides were not equal to each other. Here again, Mangle came to the rescue. On one of his family trips, Mangle had been to a country where kite fighting was the most popular sport in the land. Upon hearing this, Dwight ran home and started making plans for his own kite-fighting league.

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