Triangle Inequality Theorem

Introduction

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As a hook, ask students why the Triangle Inequality Theorem is important and how it can be applied in real-life situations. For example, you can ask them to think about situations where knowing the lengths of three sides of a triangle can determine if the triangle can actually exist or not, such as in construction or engineering projects. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the first page of the guided notes to introduce the Triangle Inequality Theorem. Walk through the key points of the theorem, including the conditions that need to be met for a triangle to be formed. Emphasize that the sum of the two shorter sides of a triangle must be greater than the length of the longest side. Show examples and non-examples to illustrate the concept. Students fill in the blanks of the vocabulary on the first page. Then, move on to discuss how to find the third possible third side length of a triangle when giving the first two side lengths.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching and have more advanced students begin working on the practice exercises.

Practice

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Have students practice the Triangle Inequality Theorem using the practice sections of the first two pages. Walk around the classroom to answer any student questions and provide assistance as needed. Then, have them start on the maze activity (page 3 of guided notes).

Fast finishers can dive into the color by number (page 4 of guided notes). You can also assign it as homework or independent work for the remainder of the class.

Real-Life Application

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Use the last page of the guided notes titled "real life applications" to bring the class back together, and introduce the concept of real-life applications of the Triangle Inequality Theorem. The Triangle Inequality Theorem is a mathematical concept that helps us understand the conditions under which triangles can be formed.

Triangle Inequality Theorem has various practical applications in our everyday lives. One such application is in the field of construction. Architects and engineers use the Triangle Inequality Theorem to ensure the stability and strength of structures. They need to consider the lengths of the sides of a triangle before constructing any beams, bridges, or supports. The theorem helps them determine if the structure will be able to withstand different forces and stresses.

The Triangle Inequality Theorem is also used in the field of computer graphics and animation. When rendering three-dimensional (3D) objects on a two-dimensional (2D) screen, the theorem helps determine if certain shapes or polygons can be displayed correctly. It ensures that the 3D objects are rendered in a way that looks realistic and visually appealing.

These examples demonstrate the practicality of the Triangle Inequality Theorem in various industries and professions. Understanding this theorem can not only help us solve mathematical problems but also provide insights into the real world around us.

Additional Self-Checking Digital Practice

If you’re looking for digital practice for the Triangle Inequality Theorem, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here’s 1 activity to explore:

• Triangle Inequality Theorem Pixel Art Google Sheets [Free!]