Lesson Plan: Pythagorean Inequality Theorem Mathematics • 8th Grade

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to determine whether an angle in a triangle is acute, right, or obtuse by using the Pythagorean inequality theorem.


Students will be able to

  • understand that in a triangle with vertices 𝐴, 𝐡, and 𝐢, if
    • (𝐴𝐢)=(𝐴𝐡)+(𝐡𝐢), then ∠𝐡 is a right angle,
    • (𝐴𝐢)>(𝐴𝐡)+(𝐡𝐢), then ∠𝐡 is an obtuse angle,
    • (𝐴𝐢)<(𝐴𝐡)+(𝐡𝐢), then ∠𝐡 is an acute angle,
  • determine the type of a triangle (acute, right, or obtuse) by using the Pythagorean inequality theorem, which involves identifying first the greatest angle in the triangle given its side lengths,
  • solve geometry problems using the Pythagorean inequality theorem.


Students should already be familiar with

  • acute, right, and obtuse angles,
  • the Pythagorean theorem.


Students will not cover

  • trigonometry.

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