A triangle is one of the most fundamental shapes in geometry. It is a closed figure formed by three line segments that connect three points which are not in a straight line. These three points are called vertices, and the line segments connecting them are called sides.
Every triangle consists of three essential components. First, we have vertices, which are the three corner points where the sides meet. These are typically labeled with capital letters like A, B, and C. Second, we have sides, which are the line segments connecting the vertices. Finally, we have angles, formed where two sides meet at each vertex.
Triangles can be classified based on their side lengths. An equilateral triangle has all three sides equal in length. An isosceles triangle has exactly two sides of equal length. A scalene triangle has all three sides of different lengths. These classifications help us understand the properties and symmetries of different triangles.
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 equal to 90 degrees, marked with a square symbol. An obtuse triangle has one angle greater than 90 degrees. Notice that in all cases, the three angles always add up to 180 degrees.
Triangles have several fundamental properties. First, the angle sum property states that all interior angles always add up to 180 degrees. Second, the triangle inequality theorem says that the sum of any two sides must be greater than the third side. Finally, an exterior angle equals the sum of the two non-adjacent interior angles. These properties are essential for solving triangle problems.