Lesson Plan: Inequality in One Triangle: Side Comparison Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to form inequalities involving the lengths of the sides of a triangle given the measures of the angles of the triangle.

Objectives

Students will be able to

  • understand that, in a triangle, when two angles have unequal measures, the side opposite the larger angle is larger than the side opposite the smaller angle,
  • form inequalities involving the lengths of the sides in a triangle by comparing the measures of the angles opposite each side,
  • understand that in a right triangle, the hypotenuse is the longest side,
  • understand that the perpendicular line segment drawn from one side of a triangle to the opposite vertex is shorter than any other line segment drawn from the same side to the same vertex,
  • prove given inequalities about lengths of sides in triangles using the opposite angles and the axioms of inequalities.

Prerequisites

Students should already be familiar with

  • the axioms of inequalities,
  • exterior angles of a triangle,
  • parallel lines and traversals,
  • the sum of angles in a triangle,
  • isosceles triangles,
  • comparing the measures of the angles in a triangle.

Exclusions

Students will not cover

  • the triangle inequality.

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