Definition of a Triangle
A triangle is a fundamental polygon in geometry defined by three straight line segments connected at three distinct points, called vertices. It is the simplest possible polygon, forming a closed, two-dimensional shape. Each pair of line segments meets at a vertex, creating an interior angle.
Key Properties of a Triangle
The most critical property of any triangle is that the sum of its three interior angles always equals 180 degrees. Additionally, the length of any side of a triangle must be less than the sum of the lengths of the other two sides (the triangle inequality theorem) and greater than their difference.
Examples of Triangles
Triangles are classified by their side lengths and angles. For instance, an equilateral triangle has three equal sides and three 60-degree angles. An isosceles triangle has two equal sides and two equal angles. A right triangle contains one angle exactly 90 degrees. Other types include scalene (all sides different) and obtuse (one angle greater than 90 degrees).
Applications of Triangles
Triangles are vital across many fields. In architecture and engineering, their rigid structure makes them ideal for building supports and trusses. In navigation, triangulation helps determine positions. In art and design, they create visual balance and direction. They are also foundational to trigonometry, a branch of mathematics used extensively in physics, surveying, and computer graphics.