Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 32

Topic

Ratios, Proportions, and Percents

Description

This example illustrates how to determine if two right triangles are not similar using proportions. Two right triangles are shown, one with legs of length 12 and 5, and the other with legs of length 35 and 15. The problem requires setting up a proportion to check for similarity: 12 / 5 = 35 / 15. After simplifying, the ratios are not equal (12 / 5 ≠ 7 / 3), concluding that the triangles are not similar.

Understanding when shapes are not similar is just as important as recognizing similarity in geometric contexts. This collection of examples helps teach the topic by presenting various scenarios where proportions are applied to determine non-similarity, allowing students to see the practical applications of these mathematical concepts in areas such as architecture, engineering, and design.

Providing multiple worked-out examples is essential for students to fully grasp the concept of similarity and non-similarity and their applications. Each example builds on previous concepts while introducing new elements, helping students develop critical thinking skills and recognize patterns across different types of proportion problems involving right triangles and other geometric figures.

Teacher's Script: "Let's examine this example where we determine that two right triangles are not similar. We'll set up the proportion 12 / 5 = 35 / 15 and simplify the ratios. Notice how the ratios are not equal, leading us to conclude that the triangles are not similar. This skill of recognizing non-similarity is crucial in many fields, including engineering and design, where understanding the limitations of scaling and proportionality is just as important as recognizing when they apply."

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