Lesson plan

5. Find that sum of angles of a triangle is 180 degrees and find informal proofs (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.Content.7.G.B.5 http://corestandards.org/Math/Content/7/G/B/5
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7
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Lesson objective: Understand that the sum of the angles of a triangle is 180°.

Students bring prior knowledge that angle measure is additive from 4.MD.C.7. When an angle is decomposed into non-overlapping parts, the angle measure of the whole angle is the sum of the angle measures of the parts. This prior knowledge is extended to informally proving the sum of the angles is 180\(^\circ\) as students manipulate angles of a triangle to determine that all three angles, when placed adjacent to each other, will form a straight angle, and therefore, 180\(^\circ\). A conceptual challenge students may encounter is that some students think that any three angles will form a triangle. 

The concept is developed through work with triangles that have been rotated to form bridge supports, which allow students to engage in productive struggle as they consider the sum of the angles for acute, obtuse, and right triangles.

This work helps students deepen their understanding of operations because the sum of the interior angles of a triangle can be justified mathematically as the sum of adjacent angles that when added form a straight angle.

Students engage in Mathematical Practice #5 (construct viable arguments and critique the reasoning of others) as they manipulate congruent triangles to informally prove the angle sum of triangles.

Key vocabulary:

  • acute angle
  • adjacent angle
  • obtuse angle
  • right angle
  • straight angle
  • supplementary angle
  • triangle angle sum

Special materials needed:

  • protractor
  • ruler