Lesson plan

8. Construct a unique triangle, many triangles, or no triangles, given attributes of a triangle (C)

teaches Common Core State Standards CCSS.Math.Content.7.G.A.2 http://corestandards.org/Math/Content/7/G/A/2
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards CCSS.Math.Practice.MP5 http://corestandards.org/Math/Practice/MP5
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Lesson objective: Understand that when given particular information about attributes of a triangle, it may be possible to construct a unique triangle, more than one triangle, or no triangle.

Students bring prior knowledge of triangles that can be categorized based on their angle types and side lengths from 4.G.A.1. This prior knowledge is extended to determine the number of triangles that will form as students draw triangles that have the given attributes. A conceptual challenge students may encounter is that sometimes more than one triangle can be drawn with a given set of conditions. 

The concept is developed through work with visual representations, which allow students to verify the triangle angle sum and the Triangle Inequality Theorem.

This work helps students deepen their understanding of operations because students will write equations to verify the angles of the triangle equal 180° and/or that the sum of the lengths of two sides of a triangle is greater than the length of the third side.

Students engage in Mathematical Practice #7 (look for and make use of structure) as they determine the conditions that create a unique triangle, more than one triangle, or no triangle. 

  • acute triangle
  • angle
  • base angle
  • isosceles triangle
  • obtuse triangle
  • right triangle
  • side
  • triangle angle sum
  • Triangle Inequality Theorem

Special materials needed:

  • protractor
  • ruler