A triangle is a polygon with three edges and three vertices. It is one of the most fundamental shapes in geometry. Every triangle has three sides that connect three corner points, called vertices. The triangle is the simplest polygon possible, as you need at least three points to enclose an area.
Triangles can be classified in different ways. By their sides, we have three main types. An equilateral triangle has all three sides of equal length. An isosceles triangle has exactly two sides of equal length. A scalene triangle has all three sides of different lengths. Each type has unique properties and appears frequently in geometry and real-world applications.
Triangles can also be classified by their angles. An acute triangle has all three angles less than 90 degrees. A right triangle has exactly one angle that equals 90 degrees. An obtuse triangle has one angle greater than 90 degrees. No matter what type of triangle it is, the sum of all three interior angles is always exactly 180 degrees. This is a fundamental property of triangles in Euclidean geometry.
Triangles have several important properties. The area of a triangle equals one half times the base times the height. The perimeter is simply the sum of all three sides. We already know that the angles always sum to 180 degrees. Another key property is the triangle inequality, which states that the length of any side must be less than the sum of the other two sides. These properties make triangles fundamental building blocks in geometry and engineering.
Triangles are fundamental shapes that appear everywhere in our daily lives. In architecture, triangular roofs provide structural strength and efficient water drainage. Bridge designs use triangular trusses because triangles are the strongest geometric shape and cannot be deformed without changing the length of their sides. Artists use triangles in compositions for visual balance. GPS systems rely on triangulation to determine precise locations. Computer graphics break down complex shapes into triangular meshes. From ancient pyramids to modern skyscrapers, triangles remain essential building blocks of our world.