Pythagorean Theorem

The smallest Pythagorean Triple is:

3, 4 and 5. 32 + 42 = 52 Calculating this becomes: 9 + 16 = 25

A Pythagorean Triple always consists of:

All even numbers, or two odd numbers and an even number.

Triangles Contain 180°

In a triangle, the three interior angles always add to 180°: A + B + C = 180°

Proof of the Pythagorean Theorem using Algebra

The area of the large square is equal to the area of the tilted square and the 4 triangles. This can be written as: (a+b)(a+b) = c2+2ab Start with: (a+b)(a+b) = c2 + 2ab Expand (a+b)(a+b): a2 + 2ab + b2 = c2 + 2ab Subtract "2ab" from both sides: a2 + b2 = c2

Hypotenuse:

The longest side of the triangle is called the "hypotenuse"

A Pythagorean Triple can never be made up of all odd numbers or two even numbers and one odd number. Because:

The square of an odd number is an odd number and the square of an even number is an even number. The sum of two even numbers is an even number and the sum of an odd number and an even number is in odd number.

In a right angled triangle:

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

Pythagoras Theorem

When a triangle has a right angle (90°) and squares are made on each of the three sides, ... ... Then the biggest square has the exact same area as the other two squares put together!

Pythagoras Theorem Equation:

a2 + b2 = c2 o... c2= a2+b2

The sides In the Pythagorean Theorem

c is the longest side of the triangle a and b are the other two sides

"Pythagorean Triple" is...

is a set of positive integers, a, b and c that fits the rule: A triangle with a Pythagorean Triple has a right angled triangle