How to Find the Shortest Side of a Triangle With Vertices

A triangle is a geometrical figure that has three sides. Several rules and theorems govern the relationship between the sides, angles and vertices of a triangle. In geometry, the shortest side of a triangle will always be located directly across from the smallest interior angle. So, to find the shortest side of a triangle, simply find the angle with the smallest vertex.

Instructions

1. Take a moment to consider your triangle. In an equilateral triangle, all of your vertices will be equal, so all of your sides will be equal. In a right triangle, one of your vertices will be equal to 90 degrees. This angle will be located directly across from your hypotenuse and longest side.

2. Find the angle of the triangle with the smallest vertex or degree. Keep in mind that the triangle inequality theorem states that the smallest angle must be equal to or smaller than 90 degrees.

3. Identify the triangle side just opposite of the smallest vertex. This is the shortest side of the triangle.

References

• Math Open Reference: Relationship of Sides to Interior Angles in a Triangle
• Math Warehouse: Triangles Side and Angles
• Free Math Help: Triangle Inequalities
• Math 'N' Stuff: Vertex, Vertices