# Lesson Plan: Inequality in One Triangle: Side Comparison Mathematics • 11th Grade

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.