The Pythagorean theorem is a fundamental principle in geometry, discovered by the ancient Greek mathematician Pythagoras. It applies to right-angled triangles and is crucial for various calculations.

Understanding the Pythagorean Theorem:

The theorem relates to the three sides of a right triangle (a triangle with one 90-degree angle).

It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Formula of the Pythagorean Theorem:

The formula is expressed as a² + b² = c², where:

a and b are the lengths of the two shorter sides of the triangle.

c is the length of the hypotenuse.

Example:

In a right triangle with sides of lengths 3 units (a) and 4 units (b), the length of the hypotenuse (c) can be calculated as follows:

Using the theorem: 3² + 4² = c².

This simplifies to: 9 + 16 = c², so c² = 25.

The length of the hypotenuse (c) is the square root of 25, which is 5 units.

Key Points to Remember:

The Pythagorean theorem only applies to right-angled triangles.

It is a useful tool in mathematics for calculating distances and in various practical applications.

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