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Chapter 9: Problem 83

In your own words, state the Pythagorean Theorem.

Short Answer

Expert verified
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The formula is: \( c^2 = a^2 + b^2 \).

Step by step solution

01

State the Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in mathematics, specifically in geometry. The theorem is named after the ancient Greek mathematician Pythagoras. The theorem states that 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. This can be written in the formula: \( c^2 = a^2 + b^2 \), where 'c' represents the length of the hypotenuse and 'a' and 'b' represent the lengths of the other two sides.

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Most popular questions from this chapter

If \(f(x)=a x^{2}+b x+c\) and \(r=\frac{-b+\sqrt{b^{2}-4 a c}}{2 a},\) find \(f(r)\) without doing any algebra and explain how you arrived at your result.

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