Inequalities in a Triangle
Overview
Inside any one triangle, the side lengths and the angle measures keep the same order: the longest side lies opposite the largest angle, and the shortest side lies opposite the smallest angle. That single idea works in both directions — given the angles, you can rank the sides, and given the sides, you can rank the angles. The reliable routine is to label each part small, medium, or large and then answer with the matches.
Vocabulary
- Opposite Side
- The side of a triangle that does not touch a given angle; the side across from the angle.
- Opposite Angle
- The angle of a triangle that does not touch a given side; the angle across from the side.
- Vertex
- The point where two sides of a triangle meet; each angle of the triangle sits at a vertex, and the side opposite that angle is the one side that does not touch the vertex.
- Congruent
- Having the same measure (for angles) or the same length (for segments).
Main Ideas
- If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.
- If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
- Simply put: the biggest side is opposite the biggest angle, and the smallest side is opposite the smallest angle.
- Sides and angles that are congruent come in matching counts — a triangle with two congruent angles has two congruent sides, and vice versa.
- Label the parts S, M, and L first, then match each side with the angle opposite it.
Lesson Notes
Flip through the notes one page at a time using the buttons below.
Lesson Video
Watch the lesson video.
Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.