why do you think Pythagorean theorem uses squares instead of other similar figures to express the relationship between the lengths of the sides in a right triangle
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http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/HeadAngela/essay1/Pythagorean.html
The Pythagorean theorem expresses a fundamental relationship between the lengths of the sides in a right triangle. It states that the sum of the squares of the lengths of the two shorter sides (known as the legs) is equal to the square of the length of the longest side (known as the hypotenuse).
The reason why the Pythagorean theorem uses squares instead of other similar figures is rooted in the geometry of a right triangle. When we square a number, we are essentially finding the area of a square with side length equal to that number.
In a right triangle, one of the angles measures 90 degrees, which means the triangle can be divided into two smaller rectangles. By using squares to represent the lengths of the sides, the Pythagorean theorem allows us to visualize the areas of these rectangles.
By squaring the lengths of the legs, we get the areas of the two smaller squares. When we add these areas together, it is equal to the area of the square formed by the hypotenuse. This concept helps us understand the geometric relationship between the sides of a right triangle.
Furthermore, using squares in the Pythagorean theorem provides a clear representation of the relationship. It allows us to easily compare and manipulate the lengths of the sides, making calculations and proofs more straightforward.
In summary, the Pythagorean theorem uses squares instead of other similar figures because it is a practical and intuitive way to express the relationship between the lengths of the sides in a right triangle, based on the geometric properties of squares and rectangles.