# Triangle

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted ${\displaystyle \triangle ABC}$.

## Parts of a Triangle

• A triangle has 3 sides. In triangle ABC, the sides are AB, BC, and CA.
• The angle formed by any two sides of a triangle is the angle of the triangle, denoted by the symbol ∠. A triangle has three angles.  The three angles of the triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A, respectively.
• The point of intersection of any two sides of a triangle is known as a vertex. A triangle has three vertices. In triangle ABC, the vertices are A, B, and C.

## Properties of a Triangle

• The sum of all three interior angles of a triangle is always equal to 180⁰.
• The sum of the length of any two sides of a triangle is always greater than the length of the third side.
• The area of a triangle is equal to half of the product of its base and height.

## Types of Triangles

Triangles can be classified based on the length of the sides or their angle measurements.

To classify triangles according to their angles, we measure each of their interior angles. Triangles can be classified by angles, as:

• Acute Triangle or Acute-angled Triangle
• Right Triangle or Right-angled Triangle
• Obtuse Triangle or Obtuse-angled Triangle
 Right Obtuse Acute ${\displaystyle \quad \underbrace {\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad } _{}}$ Oblique

The types of triangles based on the length of the sides are –

• Scalene triangle
• Isosceles triangle
• Equilateral triangle

Equilateral Triangle

Isosceles triangle

Scalene triangle

Area of a Triangle

The area of a triangle is the region that the triangle occupies in 2d space. The area of different triangles differs based on their size. If we know the base length and height of a triangle, we can determine its area. It is expressed in square units.

So, the Area of a triangle = ½ (Product of base and height of a triangle)

In the triangle PQR, PQ, QR, and RP are the sides. QR is the triangle’s base, and PS is the triangle’s height. PS is perpendicular from vertex P to the side QR. So, to find the area of △PQR, we use the following formula:

Area △PQR = ½ (Product of base and height of a triangle)

Or, Area △PQR = ½ (QR X PS)

The perimeter of a Triangle

The perimeter of a triangle is the sum of the length of all sides of the triangle.

So, the perimeter of the triangle = Sum of all three sides.

In triangle PQR, the perimeter will be the sum of the three sides, i.e., PQ, QR, and RP.

So, Perimeter of △PQR = PQ + QR + RP.