Write a statement of Pythagoras theorem and show that the 6, 8 and 10 are Pythagorean triples.

Pythagoras Theorem Statement:

The Pythagoras 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. Mathematically, this is expressed as:

c² = a² + b²

Where:

c is the length of the hypotenuse,
a and b are the lengths of the other two sides.
To Show that 6, 8, and 10 are Pythagorean Triples:

We are given the sides 6, 8, and 10. To check if these numbers form a Pythagorean triple, we need to verify if they satisfy the Pythagoras Theorem:

Identify the values for a, b, and c:

a = 6
b = 8
c = 10
Apply the Pythagoras Theorem:

c² = a² + b²
10² = 6² + 8²
100 = 36 + 64
100 = 100
Since both sides of the equation are equal, the sides 6, 8, and 10 satisfy the Pythagoras Theorem, meaning they form a Pythagorean triple.

Therefore, 6, 8, and 10 are Pythagorean triples.