A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. Each triangle has three sides connecting three corner points, and three interior angles where the sides meet.
Triangles can be classified in different ways. By their sides, we have equilateral triangles with all sides equal, isosceles triangles with two sides equal, and scalene triangles with all sides different. By their angles, we have acute triangles where all angles are less than ninety degrees, right triangles with one angle exactly ninety degrees, and obtuse triangles with one angle greater than ninety degrees.
Triangles have several important properties. The sum of all interior angles in any triangle is always one hundred eighty degrees. The triangle inequality states that the sum of any two sides must be greater than the third side. The perimeter is the sum of all three sides, and the area can be calculated as one half times base times height.
The Pythagorean theorem is one of the most famous theorems in mathematics. It states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. This can be written as a squared plus b squared equals c squared, where a and b are the legs and c is the hypotenuse. This theorem has countless applications in mathematics, physics, and engineering.
To summarize what we have learned about triangles: They are three-sided polygons that can be classified by their sides or angles. All triangles have interior angles that sum to one hundred eighty degrees. The Pythagorean theorem is a fundamental property of right triangles. Triangles are essential geometric shapes with many practical applications in mathematics and science.