# What is a triangle

## 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.

Calculate triangle area by length of its sides

Calculate triangle angles by length of its sides