Triangles

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

Types of Triangles

  1. Equilateral Triangle: A triangle with all three sides of equal length. All three angles are also equal, each being 60 degrees.
  2. Isosceles Triangle: A triangle with two sides of equal length. The angles opposite these sides are also equal.
  3. Scalene Triangle: A triangle in which all three sides have different lengths, and all three angles are also different.
  4. Right Triangle: A triangle in which one of the angles is a right angle (90 degrees). The side opposite to the right angle is the hypotenuse, which is the longest side in the right triangle.
  5. Obtuse Triangle: A triangle in which one of the angles is an obtuse angle (greater than 90 degrees).
  6. Acute Triangle: A triangle in which all the angles are acute angles (less than 90 degrees).

Properties of Triangles

  1. Sum of Angles: The sum of the angles in a triangle is always 180 degrees.
  2. Pythagorean Theorem: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This is stated as a² + b² = c², where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

Applications

Triangles are used extensively in various fields including geometry, trigonometry, architecture, physics, engineering, computer graphics, and more. They are fundamental in the study of trigonometric functions and in the calculation of areas and volumes of other geometric shapes.