Math Example--Right Triangles-- Example 23

Topic

Right Triangles

Description

This example presents an isosceles right triangle with angles 45°, 45°, and 90°. The hypotenuse is labeled √(2) * x, one leg is labeled x, and the other leg is labeled b. Using the Pythagorean Theorem, we find that b = √((√(2) * x)² - x²) = √(x^2) = x. This demonstrates the general case for 45-45-90 triangles, where both legs are equal and the hypotenuse is √(2) times the leg length.

This example generalizes the concept of 45-45-90 triangles, showing how the relationship between sides can be expressed algebraically for any scale factor x. It helps students understand the algebraic representation of geometric relationships and how variables can be used to express general rules in mathematics.

Providing multiple worked examples is crucial for students to fully grasp the concept of right triangles and their various applications. Each new example offers an opportunity to explore different aspects of right triangles, helping students develop problem-solving skills and a deeper understanding of geometric relationships.

Teacher's Script: Let's examine our twenty-third example. We have an isosceles right triangle where the sides are expressed in terms of a variable x. How is this different from our previous examples? That's right, we're looking at a general case. Our task is to express b in terms of x. As we work through this, think about how this relates to the specific 45-45-90 triangles we've seen. How does using variables help us understand the general properties of these special triangles?

For a complete collection of math examples related to Right Triangles click on this link: Math Examples: Right Triangles Collection.