A triangle is a closed, two-dimensional shape, specifically a three-sided **polygon**. This means it has three straight sides, three angles, and three vertices.

The term “**triangle**” originates from the Latin word “triangulum,” which means “three-cornered” or “having three angles.” The name perfectly describes the fundamental characteristic of this shape – it is defined by the presence of three angles formed by its three sides.

## Why it’s called a “triangle”

**Triangular Sides**: The prefix “tri-” refers to three, and the sides of a triangle consist of precisely three straight line segments.**Angles**: The suffix “-angle” denotes the presence of angles. Since a triangle is a three-sided polygon, it inherently possesses three angles formed at its vertices.

These three angles and three sides give a triangle its unique properties and make it one of the simplest and most widely studied shapes in **geometry**.

## Types of Triangles

- Types of Triangles based on Sides:
**Equilateral Triangle**: All three sides are of equal length.**Isosceles Triangle**: Two sides are of equal length.**Scalene Triangle**: All three sides have different lengths.

- Types of Triangles based on Angles:
**Acute Triangle**: All three angles are less than 90 degrees.**Right Triangle**: One angle is exactly 90 degrees.**Obtuse Triangle**: One angle is greater than 90 degrees.

## Some Key Points About Triangles

**Sides and Vertices**: A triangle has three sides, which are line segments connecting three non-collinear points. The three points where the sides intersect are called vertices.**Angle Sum**: The sum of the interior angles of a triangle is always 180 degrees. This property is known as the Triangle Sum Theorem.- Area of a Triangle: The area of a triangle can be calculated using different formulas, depending on the given information (e.g., base and height, three sides, etc.). The most common formula is

**Area** = (1/2) × **base** × **height**

- The perimeter of a triangle can be calculated using the formula:

**Perimeter** = **sum of the side lengths**

- The
**centroid of a triangle**is the point where the three medians of the triangle intersect. The centroid divides each median in the**ratio 2:1**. - The
**orthocenter of a triangle**is the point where the three altitudes of the triangle intersect. The altitudes are lines that are perpendicular to a side of the triangle and pass through the opposite vertex. - The circumcenter of a triangle is the point where the three circumcircles of the triangle intersect. The circumcircle of a triangle is the circle that passes through all three vertices of the triangle.

Triangles play a fundamental role in various mathematical principles and real-world scenarios, making them an essential concept for students and professionals across different fields.