Lesson Plan

6. Right triangles within other polygons (A)

teaches Common Core State Standards CCSS.Math.Content.8.G.B.6 http://corestandards.org/Math/Content/8/G/B/6
teaches Common Core State Standards CCSS.Math.Content.8.G.B.7 http://corestandards.org/Math/Content/8/G/B/7
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4
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Lesson objective: Connect work with right triangles to include right triangles contained in other shapes.

This lesson provides an opportunity for students to apply their knowledge and understanding of the converse of the Pythagorean Theorem to a real-life situation. Students are asked to decide if certain polygons contain right angles by checking for right triangles within those polygons.

Key Concept students will use: 

  • If the sum of the squares of the measures of two legs of a triangle is the same as the square of the length of the third side, the triangle must be a right triangle.

Skills students will use:

  • classify shapes by their properties (Grade 5, Unit 11)
  • apply the converse of the Pythagorean Theorem to check for right triangles and right angles.

Students engage in Mathematical Practice 3 (construct viable arguments and critique the reasoning of others) as they evaluate Mrs. Romero's and Diego's methods for understanding right angles, and apply a viable method to other situations.

Key vocabulary: 

  • degrees
  • diagonal
  • hypotenuse
  • legs
  • polygon
  • Pythagorean Theorem
  • right angle
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