Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in geometry that describes the relationship between the sides of a right-angled triangle. 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 lengths of the other two sides.

Formula

The Pythagorean Theorem can be expressed using the following formula:

c² = a² + b²

Where:

• c is the length of the hypotenuse
• a and b are the lengths of the other two sides

Example

For example, if a right-angled triangle has side lengths of 3 and 4, the length of the hypotenuse can be found using the Pythagorean Theorem:

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = √25

c = 5

Applications

The Pythagorean Theorem is widely used in various fields, including architecture, engineering, and physics. It allows for the calculation of distances, the determination of right angles, and the construction of square and rectangular shapes.

Study Guide

When studying the Pythagorean Theorem, it is important to:

1. Understand the concept of a right-angled triangle and its properties.
2. Memorize the formula c² = a² + b².
3. Practice solving problems involving the calculation of side lengths using the theorem.
4. Explore real-world applications of the theorem to appreciate its practical significance.

By mastering the Pythagorean Theorem, you will develop a strong foundation in geometry and be equipped to solve a wide range of mathematical and practical problems.

[Pythagorean Theorem] Related Worksheets and Study Guides:

• The Pythagorean TheoremMathematics • Seventh Grade