Lesson plan

5. Understand triangle angle sum using similar triangles (C)

teaches Common Core State Standards CCSS.Math.Content.8.G.A.5 http://corestandards.org/Math/Content/8/G/A/5
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 the triangle angle sum using similar triangles.

Students bring prior knowledge of similarity from 8.G.4 and angle-angle criterion from 8.G.B.5.  This prior knowledge is extended to the sum of the interior angles of a triangle as students use similar triangles and rigid transformations to prove informally the angle sum of triangles. A conceptual challenge students may encounter is using corresponding angles to justify their thinking. 

The concept is developed through work with similar triangles derived from Sierpinski's Triangle, which allows students to engage in productive struggle as they extend parallel lines and use corresponding angles and the angle-angle criterion to prove informally the angle sum of triangles.

This work helps students deepen their understanding of operations because the sum of interior angles of triangles can be justified mathematically as the sum of corresponding angles of similar triangles.

Students engage in Mathematical Practice 5 (use math tools strategically) as they determine similar triangles and engage in productive struggle to manipulate them and create an informal proof of the triangle angle sum.

Key vocabulary:

  • angle-angle criterion
  • angle sum of triangles
  • corresponding angles
  • similar triangles

Special materials needed:

  • template of Sierpinski's Triangle