The tangram is a fascinating ancient Chinese puzzle made of seven geometric pieces. These seven pieces can be arranged to form a perfect square, and amazingly, they can also create thousands of different shapes including animals, people, and objects.
Let's analyze the geometric properties of each tangram piece. All pieces are based on right triangles with forty-five degree angles. The two large triangles are identical, each with an area of two units. The medium triangle has an area of one unit. The two small triangles, square, and parallelogram each have an area of half a unit. These proportional relationships are key to understanding how the pieces fit together to form the complete square.
Now let's learn the strategy for forming a square with tangram pieces. We start by positioning the two large triangles as our foundation, as they form exactly half of the target square. Then we systematically add the remaining five pieces, using their geometric relationships to guide proper placement. This methodical approach ensures we can reliably reconstruct the square formation.
Let's watch the complete step-by-step assembly process. We start with the target square outline, then place each piece systematically. First, the two large triangles form the foundation. Next, we add the medium triangle, followed by the two small triangles. Then we position the square piece, and finally complete the puzzle with the parallelogram. Each step builds upon the previous one, creating a perfect square.
The tangram puzzle demonstrates remarkable flexibility - there are multiple valid ways to arrange the seven pieces into a perfect square. Here we see three different solutions. Solution A shows the standard arrangement we learned earlier. Solution B uses rotated pieces in different positions. Solution C presents a mirrored pattern. All three arrangements use the exact same seven pieces and form identical squares, demonstrating the concept of geometric equivalence. This flexibility showcases the rich mathematical properties that make the tangram such a fascinating and enduring puzzle.