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The Pythagorean Theorem is a fundamental principle in geometry that establishes a relationship between the sides of a right-angled triangle. While it is often stated as a mathematical equation, its visual derivation offers an intuitive understanding of its significance.
In a visual derivation of the Pythagorean Theorem, one begins with a right-angled triangle, where one angle is precisely 90 degrees. The triangle is typically depicted with sides labeled as 'a', 'b', and 'c'. 'a' and 'b' represent the two shorter sides, known as the legs, while 'c' denotes the longest side, known as the hypotenuse.
To visually demonstrate the theorem, we start by forming squares on each of the three sides of the triangle. The square on side 'a' has an area of 'a²', the square on side 'b' has an area of 'b²', and the square on side 'c' has an area of 'c²'.
Next, we observe how these squares fit together. The square on side 'c', the hypotenuse, is constructed by placing squares on sides 'a' and 'b'. The area of this square should be equal to the sum of the areas of the squares on sides 'a' and 'b', or 'a² + b²'.
This visual representation demonstrates that the area of the square formed by the hypotenuse is indeed equal to the sum of the areas of the squares formed by the other two sides. Mathematically, this is expressed as:
c² = a² + b²
This equation is the Pythagorean Theorem, named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.
The visual derivation of the Pythagorean Theorem not only provides a geometric understanding of the relationship between the sides of a right triangle but also offers insight into the elegance and universality of mathematical principles. It serves as a foundational concept in mathematics and finds applications in various fields, from engineering to physics and beyond.
Video Edited by:
Name - Mayank Ranjan
Email - renexier.techygame.yt@gmail.com
LinkedIn link - shorturl.at/afgnJ
Wrong Math
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