Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 29

Topic

Ratios, Proportions, and Percents

Description

This example demonstrates how to determine if two triangles are similar using proportions. Two triangles are shown, both with a 70° angle. The first triangle has sides of 12 and 10, while the second has sides of 18 and 15. The problem requires setting up a proportion to check for similarity: 12 / 10 = 18 / 15. After simplifying, both ratios are equal (6 / 5 = 6 / 5), confirming that the triangles are indeed similar.

Understanding similarity in geometric contexts, particularly with triangles, is a fundamental skill in mathematics. This collection of examples helps teach the topic by presenting various scenarios where proportions are applied to determine similarity, allowing students to see the practical applications of these mathematical concepts in areas such as architecture, engineering, and design.

Exposure to multiple worked-out examples is crucial for students to fully grasp the concept of similarity and its applications. Each example reinforces the core concept while introducing different geometric scenarios, helping students develop problem-solving skills and recognize patterns across various types of similarity problems involving triangles and other geometric figures.

Teacher's Script: "In this example, we're determining if two triangles are similar by setting up a proportion. Notice how we compare the ratios of corresponding sides. Let's solve this step-by-step, showing you how to apply proportion concepts to determine similarity. This skill will be valuable in many areas of mathematics, including trigonometry, scaling in design, and solving problems in physics and engineering where similar shapes are often encountered."

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