Master the fundamentals of triangles - the most important shape in geometry. Learn definitions, properties, and see how triangles appear everywhere in our world.
A triangle is a polygon with three vertices, three sides, and three interior angles. It is the simplest polygon possible and forms the building block of many complex geometric shapes.
Corner points where two sides meet
Line segments connecting vertices
Interior angles that always sum to 180°
The sum of all interior angles in any triangle is always 180°.
Example: If two angles are 60° and 70°, the third must be 50°
The sum of any two sides must be greater than the third side.
Example: Sides 3, 4, 5 work because 3+4>5, 3+5>4, 4+5>3
Triangles cannot be deformed without changing side lengths - they're inherently stable.
This is why triangles are used in construction and engineering
A triangle is the polygon with the fewest possible sides.
Any polygon can be divided into triangles
House roofs are often triangular because triangles are the most stable geometric shape. The three sides distribute weight evenly.
Yield signs are equilateral triangles - all sides equal, all angles 60°. This shape is easily recognizable from any direction.
Bridge trusses use triangles because they cannot be deformed without changing the length of sides - they're rigid.
Test your understanding with interactive triangle calculators and problem-solving tools.
Explore more advanced triangle concepts and classifications.