Statement: The Pythagorean theorem states that in a right triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the ot...
Statement: The Pythagorean theorem states that in a right triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides (legs).
Proof:
Suppose a right triangle has sides with lengths a, b, and c, where c is the hypotenuse. The Pythagorean theorem states that:
This means that the square of the longest side is equal to the sum of the squares of the other two sides.
Examples:
In a right triangle with sides 3, 4, and 5, the Pythagorean theorem holds true.
In a right triangle with sides 6, 8, and 10, the Pythagorean theorem also holds true.
In a right triangle with sides 12, 13, and 14, the Pythagorean theorem does not hold true