Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as c² = a² + b².

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs of a right triangle, while 'c' represents the length of the hypotenuse.

To calculate the length of the hypotenuse (c), use the formula c = √(a² + b²), where a and b are the lengths of the other two sides.

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 units.

In a right triangle, the sum of the squares of the lengths of the two legs (a and b) is equal to the square of the length of the hypotenuse (c): a² + b² = c².

No, the Pythagorean Theorem only applies to right triangles.

If the hypotenuse (c) and one leg (a) are known, the other leg (b) can be found using the formula b = √(c² - a²).

Using the Pythagorean Theorem: c = √(10² + 25²) = √(100 + 625) = √725 ≈ 26.93 feet.

The Pythagorean Theorem is used in various real-life applications, such as construction, navigation, and physics, to determine distances and relationships between different points.

The converse of the Pythagorean Theorem states that if a triangle has sides of lengths a, b, and c, and if a² + b² = c², then the triangle is a right triangle.