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Chapter 10: Problem 54

In your own words, state the Pythagorean Theorem.

Short Answer

Expert verified
The Pythagorean theorem, in simple terms, states that in a right-angled triangle, the square of the longest side equals the sum of the squares of the other two sides.

Step by step solution

01

Understand the terms

In geometry, a right triangle is a triangle in which one angle is a right angle (90 degrees). The sides of a right triangle are called the base, perpendicular, and hypotenuse. The hypotenuse is the side opposite the right angle, and it is the longest side.
02

Pythagoras' Theorem Original Statement

Pythagoras' theorem originally states that in any 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. This can be written as \(a^{2} + b^{2} = c^{2}\), where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
03

Rewording Pythagoras' Theorem

Given this understanding, in simpler words, the theorem can be stated as: 'For any triangle that has a right angle (90 degrees), the square of the longest side equals the sum of the squares of the other two sides.'

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