## triangle

### In mathematics, a triangle is a geometric shape that consists of three line segments connected together to form a closed figure

In mathematics, a triangle is a geometric shape that consists of three line segments connected together to form a closed figure. These line segments are called sides of the triangle.

Here are some key concepts and properties related to triangles:

1. Types of triangles: Triangles can be classified into different types based on their angles and sides.

– Based on angles: A triangle can be classified as acute, right, or obtuse. In an acute triangle, all angles are less than 90 degrees. In a right triangle, one angle is exactly 90 degrees. In an obtuse triangle, one angle is greater than 90 degrees.

– Based on sides: A triangle can be classified as equilateral, isosceles, or scalene. An equilateral triangle has all three sides of equal length. An isosceles triangle has two sides of equal length. A scalene triangle has all three sides of different lengths.

2. Triangle inequality theorem: This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with side lengths a, b, and c, a + b > c, a + c > b, and b + c > a.

3. Interior angles of a triangle: The interior angles of a triangle are the angles formed inside the triangle. The sum of the interior angles of a triangle is always 180 degrees. This property is known as the angle sum property of triangles.

4. Pythagorean theorem: The Pythagorean theorem is a fundamental result in geometry that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In equation form, it is given as a^2 + b^2 = c^2, where c represents the hypotenuse and a, b represent the other two sides.

5. Area of a triangle: The area of a triangle can be calculated using various formulas based on the given information. One commonly used formula is the formula for the area of a triangle using the base and height, which is given as A = (1/2) * base * height.

These are just a few key concepts related to triangles. Triangles are a fundamental concept in geometry and have many more properties and theorems associated with them.

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