A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. Every triangle has three sides, three corners called vertices, and three angles. The vertices are typically labeled with letters like A, B, and C.
Triangles can be classified in different ways. By their sides, we have equilateral triangles with all sides equal, isosceles triangles with two equal sides, and scalene triangles with all different sides. By their angles, we have acute triangles where all angles are less than 90 degrees, right triangles with one 90-degree angle, and obtuse triangles with one angle greater than 90 degrees.
Triangles have several important properties. The sum of all interior angles in any triangle is always 180 degrees. The triangle inequality states that the sum of any two sides must be greater than the third side. The area of a triangle can be calculated using the formula: area equals one-half times base times height. The perimeter is simply the sum of all three sides.
Triangles are central to many important mathematical theorems. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides. The Law of Sines relates the sides of any triangle to the sines of their opposite angles. The Law of Cosines generalizes the Pythagorean theorem for any triangle. These theorems are fundamental tools in geometry and trigonometry.
A triangle is one of the most fundamental shapes in geometry. It is a polygon with exactly three sides, three vertices or corners, and three interior angles. The most important property of triangles is that the sum of their interior angles is always 180 degrees, regardless of the triangle's shape or size.
Triangles can be classified by their side lengths. An equilateral triangle has all three sides of equal length, making it perfectly symmetrical. An isosceles triangle has exactly two sides of equal length. A scalene triangle has all three sides of different lengths, making it the most general type of triangle.
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, which is marked with a small square. An obtuse triangle has one angle greater than 90 degrees.
Triangles have several important properties and formulas. The area equals half the base times the height. The perimeter is the sum of all three sides. All interior angles sum to 180 degrees. The triangle inequality states that the sum of any two sides must be greater than the third side for a valid triangle.
Triangles have countless real-world applications. In architecture and construction, triangular trusses provide structural strength for roofs and bridges because triangles are inherently stable shapes. In navigation and surveying, triangulation using GPS satellites helps determine precise locations. In computer graphics, complex 3D models are built from thousands of triangular faces, making triangles fundamental to modern digital visualization and gaming.