Geometry

Lesson 13

Objective

Determine if three side lengths will create a unique triangle or no triangle. 

Common Core Standards

Core Standards

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  • 7.G.A.2 — Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Criteria for Success

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  1. Investigate creating triangles with different side lengths.
  2. Understand why a triangle cannot be created if the sum of two side lengths is less than the third side. 
  3. Determine if a given set of side lengths will create a triangle.
  4. Determine a measure of a third side length, given two other sides of a triangle.

Tips for Teachers

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The following materials are needed for this lesson: AngLegs or wooden skewers (see the blog post Triangle Inequality Skewers by Elissa Miller), compasses, rulers.

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Anchor Problems

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Problem 1

Using AngLegs or wooden skewers, investigate different side lengths that will create a triangle.  

Complete the chart below, adding rows as needed.

Side length $$a$$ Side length $$b$$ Side length $$c$$ Triangle? If not, explain why
       
       
       

What conclusion can you make about the side lengths of a triangle? 

Guiding Questions

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Problem 2

In each diagram below, line segment $${AB}$$  is 4 units. Two circles are drawn with a given radius and center at point $$A$$ and point $$B$$.

Diagram 1:

Circle with center $$A$$ has a radius of 4 units.

Circle with center $$B$$ has a radius of 2 units.

Diagram 2:

Circle with center $$A$$ has a radius of 1 unit.

Circle with center $$B$$ has a radius of 2 units.

 

 

  1. Using Diagram 1, explain or show why you can create a triangle with side lengths 4 units, 4 units, and 2 units. 
  2. Using Diagram 2, explain or show why you cannot create a triangle with side lengths 4 units, 1 unit, and 2 units. 

Guiding Questions

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Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Target Task

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Problem 1

Which of the following set of side lengths could not be used to create a triangle?

  1. 2 cm, 6 cm, 7 cm
  2. 3 cm, 3 cm, 3 cm
  3. 4 cm, 5 cm, 8 cm
  4. 5 cm, 7 cm, 12 cm

Problem 2

A triangle has two side lengths that measure 6 in. and 9 in. Which of the following could be the measure of the third side? Select all that apply.

  1.   3
  2.   4
  3.   8
  4.   11
  5.   14
  6.   15
  7.   18

Mastery Response

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