Lesson Plan: Introduction to Inequalities in Triangles Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to understand the concept of inequality in general, define the axioms of inequalities, and compare between the measures of angles in triangles.


Students will be able to

  • form inequalities for the angles and sides in a triangle,
  • understand and use the axioms of inequality which state that
    • if 𝑥>𝑦, then 𝑥+𝑧>𝑦+𝑧,
    • if 𝑥>𝑦, then 𝑥𝑧>𝑦𝑧,
    • if 𝑥>𝑦 and 𝑧>0, then 𝑥𝑧>𝑦𝑧,
    • if 𝑥>𝑦 and 𝑦>𝑧, then 𝑥>𝑧,
    • if 𝑥>𝑦 and 𝐴>𝐵, then 𝑥+𝐴>𝑦+𝐵,
  • use the axioms of inequalities to solve problems about triangles.


Students should already be familiar with

  • algebraic inequalities,
  • the angle sum of a triangle,
  • isosceles triangles.


Students will not cover

  • the triangle inequality.

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