# 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.