## Triangle and Polygon

**A polygon** is indeed a 2-dimensional shape composed of straight sides, and by definition, it must have at least three sides. **A triangle**, being the simplest polygon, has exactly three sides and three angles. Therefore, it meets the criteria of being a polygon with the least number of sides, which is three.

**A triangle** is a polygon with three sides, three vertices, and three angles. It is one of the simplest shapes in geometry.

## Type of triangle

We can group the types of triangles based on their side lengths and angle measures:

By Side Length:

**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.

By Angle Measure:

**Acute Triangle**: All angles are acute (less than 90 degrees).**Right Triangle**: One angle is a right angle (measuring 90 degrees).**Obtuse Triangle**: One angle is obtuse (greater than 90 degrees).

## Properties of triangle

Triangles possess several properties, which are fundamental to their geometric nature and mathematical characteristics. Here are some key properties of triangles:

**Three Sides**: A triangle has exactly three sides.

**Three Angles**: A triangle has exactly three angles. The sum of the angles in any triangle is always 180 degrees.

**Triangle Inequality Theorem**: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

**Exterior Angle Theorem**: The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

**Angle Sum Property**: The sum of the interior angles of a triangle is always 180 degrees.

**Types by Angle Measure**:

- Acute Triangle: All angles are less than 90 degrees.
- Right Triangle: One angle is exactly 90 degrees.
- Obtuse Triangle: One angle is greater than 90 degrees.

**Types by Side Length**:

- Equilateral Triangle: All sides are equal.
- Isosceles Triangle: Two sides are equal.
- Scalene Triangle: All sides are different.

**Height (Altitude)**: A perpendicular line segment drawn from one vertex to the opposite side (or its extension) is called the altitude of the triangle.

**Median**: A line segment connecting a vertex of the triangle to the midpoint of the opposite side is called a median. Each triangle has three medians, which intersect at the centroid of the triangle.

**Perimeter**: The perimeter of a triangle is the sum of the lengths of its three sides.

**Area**: The area of a triangle can be calculated using various formulas, such as

(1/2) × base × height, Heron's formula, or by trigonometric methods.