Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in mathematics that relates to the lengths of 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 represented by the following formula:

c² = a² + b²

Where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

Application

The Pythagorean Theorem is commonly used to find the length of one side of a right-angled triangle when the lengths of the other two sides are known. It is also used in various fields such as architecture, engineering, and physics to solve problems involving right-angled triangles.

Study Guide

To understand and apply the Pythagorean Theorem effectively, it is essential to grasp the following concepts:

1. Right-Angled Triangles: Understand the properties of right-angled triangles, including the relationship between the lengths of the sides and the angles.
2. Squaring Numbers: Be familiar with the concept of squaring a number and the notation used for representing squared values.
3. Substitution and Simplification: Practice substituting the given values into the Pythagorean Theorem formula and simplifying the equation to solve for the unknown side length.
4. Real-World Applications: Explore real-world examples and problems that involve using the Pythagorean Theorem to find unknown side lengths in practical situations.

Problem-Solving Steps

When applying the Pythagorean Theorem to solve a problem, follow these steps:

1. Identify the hypotenuse and the other two sides of the right-angled triangle.
2. Substitute the given side lengths into the Pythagorean Theorem formula.
3. Square the side lengths, add the squared values, and set up the equation c² = a² + b².
4. Solve for the unknown side length by taking the square root of the sum of the squared values on one side of the equation.
5. State the final answer with appropriate units and rounding if necessary.

By understanding the Pythagorean Theorem and practicing its application, you can confidently solve problems involving right-angled triangles and develop a deeper understanding of geometric relationships.

[Pythagorean Theorem] Related Worksheets and Study Guides:

• The Pythagorean TheoremMathematics • Seventh Grade