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State and prove the Pythagoras theorem....

State and prove the Pythagoras theorem.

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**Pythagoras Theorem Statement:** In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, this can be expressed as: \[ AC^2 = AB^2 + BC^2 \] where \( AC \) is the hypotenuse, and \( AB \) and \( BC \) are the other two sides. **Proof of the Pythagorean Theorem:** 1. **Consider a Right-Angled Triangle:** ...
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