## triangle

### In geometry, a triangle is a polygon with three sides, three vertices (or corners), and three angles

In geometry, a triangle is a polygon with three sides, three vertices (or corners), and three angles. Triangles are one of the fundamental shapes in mathematics and have been studied for centuries.

The sides of a triangle are typically denoted as AB, BC, and CA, where A, B, and C are the vertices. The angles formed by the sides of the triangle are denoted by capital letters, such as ∠A, ∠B, and ∠C. The sum of the angles in any triangle is always 180 degrees.

Based on the lengths of its sides, triangles can be classified into different types:

1. Equilateral Triangle: A triangle with all three sides and angles equal in length and measure, respectively.

2. Isosceles Triangle: A triangle with two sides of equal length. This implies that two angles are equal as well.

3. Scalene Triangle: A triangle with all three sides of different lengths. The angles in a scalene triangle are also different.

Triangles can also be classified based on the measures of their angles:

1. Acute Triangle: A triangle with all three angles measuring less than 90 degrees.

2. Right Triangle: A triangle with one angle measuring exactly 90 degrees. The side opposite the right angle is called the hypotenuse.

3. Obtuse Triangle: A triangle with one angle measuring more than 90 degrees.

Additionally, triangles can be classified as congruent if they have the exact same shape and size. Congruent triangles have corresponding sides and angles that are equal.

Triangles also have various properties and theorems, such as the Pythagorean theorem, triangle inequality theorem, and various trigonometric ratios, which are used to solve various mathematical problems involving triangles.

Overall, triangles are an important concept in geometry, and their properties and classifications play a significant role in the study of mathematics.

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