Once upon a time, in a small and vibrant city called Geometrópolis, a group of four young adventurers loved to explore the mysteries of the world around them. In Geometrópolis, all the buildings, streets, and even the parks were constructed with perfect geometric shapes that dazzled the eyes and challenged the mind. However, there was a mysterious secret hidden in the city, that only the most curious and brave could discover.
The heroes of this story were bright students and close friends: Ana, Pedro, Luiza, and João. One day, these adventurers received a special mission from the legendary Master Polygon, a wise elder known for his vast knowledge of geometry and for his long white beard that almost touched the ground. He summoned them to his crystalline polyhedral tower and explained a threat looming over the harmony of Geometrópolis. An enigmatic force was altering the size of geometric figures, creating true chaos in the city.
"Their angles remain the same, but something strange is happening with their sides and areas," Master Polygon explained with a worried expression. "You need to use your mathematical skills to restore balance." Without hesitation, the young adventurers accepted the mission with enthusiasm. Equipped with their smartphones and tablets, they began a journey through the city utilising a fascinating augmented reality app that allowed them to see geometric figures in 3D. Every time they encountered a distorted figure, there was a challenge to solve.
In the first challenge, they came across an ancient square in the centre of the main square that had been mysteriously enlarged. Pedro, the most observant in the group, quickly realised it was a proportionality problem. "When we enlarge the sides of a square, the area does not change in the same proportion," he noted. With his calculation skills, Pedro demonstrated that by doubling the side of the square, the area multiplied by four. As soon as they recalculated the correct proportion, the square returned to its original size and revealed a secret clue for the next challenge.
Next, the adventurers arrived at the charming Triangle Park, where the triangles, once perfect, now varied in size. With her keen observation, Ana noticed that, despite the triangles being different sizes, their angles remained unchanged. "This is angle congruence!" she exclaimed excitedly. "Even if the size of the triangles changes, their angles are always the same." With this information, the group applied proportionality to restore the triangles to their original shape, bringing them another clue and a sense of accomplishment.
As they explored the lovely town, the students began documenting their discoveries in short videos and stories, sharing everything on a fictional social network called GeoGrama. Their goal was to help other children in Geometrópolis understand the importance of angle congruence and proportionality. They used editing apps like InShot and CapCut to make their content more engaging and educational, ensuring that learning was, above all, fun.
At the end of their exciting journey, our heroes reached the majestic Tower of Proportionality, where Master Polygon awaited them with one last challenging riddle. They needed to design a mini-city using the 3D design software Tinkercad, applying everything they had learned about angle congruence and proportionality. Working together, our young adventurers designed a city where every building respected these mathematical rules, thus restoring harmony in Geometrópolis.
The inhabitants of Geometrópolis celebrated with great joy the victory of the young heroes, who were now known as the Defenders of Geometry. They taught everyone that, both in mathematics and in life, understanding the relationships between things can help us solve problems and bring balance. And so, Geometrópolis became a city of perfect geometric harmony once again, thanks to the courage, dedication, and intelligence of Ana, Pedro, Luiza, and João.
And you, young adventurer, are you ready to embark on your own geometric journey? Answer the questions below and uncover the secrets of Geometrópolis:
What happens to the area of a square when we double its sides? How do the angles of a shape change when we increase its size? Can you give an example of using proportionality and angle congruence in the real world? How can technology help us better understand these mathematical concepts?
Good luck, and remember: the journey is just as important as the destination!
