Exploring the Triangle Inequality Theorem

Objective:

Students will be able to apply the Triangle Inequality Theorem by determining if a given set of side lengths can form a triangle or not.

Assessment:

Create a worksheet with various sets of side lengths and ask students to identify which ones can form a triangle according to the Triangle Inequality Theorem.

Key Points:

• Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides of lengths a, b, and c, the following inequalities must hold true:

  • a + b > c

  • a + c > b

  • b + c > a

• Understanding and applying the Triangle Inequality Theorem is essential in determining the validity of a triangle.

• Incorrect application of the theorem can lead to misidentifying triangles.

Opening:

• Start the lesson by showing students images of different shapes and asking them to identify which ones are triangles.

• Engage students with a discussion on what makes a shape a triangle.

Introduction to New Material:

• Explain the Triangle Inequality Theorem using concrete examples and visual aids.

• Emphasize the meaning of the theorem through real-world scenarios.

• Common Misconception: Students might think that any three line segments can form a triangle, which is not true.

Guided Practice:

• Provide students with various sets of side lengths and guide them through determining if they can form a triangle using the theorem.

• Scaffold questioning from simple cases to more complex ones.

• Monitor student performance by circulating the classroom and providing support as needed.

Independent Practice:

• Assign a worksheet where students have to apply the Triangle Inequality Theorem to identify if the given side lengths can form a triangle.

• Encourage students to justify their answers and explain their reasoning.

Closing:

• Have students share their responses to the independent practice worksheet.

• Summarize the key points of the lesson about the Triangle Inequality Theorem.

Extension Activity:

• For students who finish early, provide a challenge where they have to create their own sets of side lengths and determine if they form valid triangles.

Homework:

• Ask students to find real-life examples where the Triangle Inequality Theorem would be applicable and write a brief explanation for each.

Standards Addressed:

• CCSS.MATH.CONTENT.HSG.CO.D.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

• CCSS.MATH.CONTENT.HSG.CO.D.13: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.