What is Properties of Triangle. Types and Formulas with Examples

A triangle is a two-dimensional figure bound by three sides. It is a polygon with three sides, three angles, and three vertices formed by adjacent sides. The properties of a triangle vary in its types.

Different properties characterize a triangle:

• Angle sum property
  The sum of all the interior angles of a triangle is equal to 180 degrees. An equilateral triangle has three equal interior angles so each of the angles measures 60 degrees.

• Exterior angle property
  If any side of a triangle is extended, the exterior angle formed is equal to the sum of two opposite interior angles. This property is derived from the angle sum property only.

• Side inequality property
  In a triangle, the sum of any two sides will be always greater than the third side.

• Right-angle triangle property
  In a right-angled triangle, the square of the side opposite to the right-angle is equal to the sum of the squares of the other two sides. This relationship is called the Pythagoras theorem.

• Area of triangle
  The area of a triangle is calculated by the formula: Area = ½ * Base* Height

• Greatest side property
  The greatest side of a triangle is the side opposite to the greatest angle. In an isosceles triangle, the two angles opposite to the two equal sides are also equal.

Types of Triangle

Triangles can be classified according to the dimension of sides and their relationship. Triangles can also be classified based on their interior angles.
Triangles can be classified into the following types based on the sides:

1. Equilateral Triangle: It is a triangle having three equal sides.

2. Isosceles Triangle: It is a triangle with two equal sides.

3. Scalene Triangle: It is a triangle in which all sides are unequal.

Triangles can be classified into the following types based on the angles:

1. Acute Triangle: A triangle having all interior angles less than 90 degrees

2. Right-angle Triangle: A triangle in which one angle is equal to 90 degrees

3. Obtuse Triangle: a triangle in which one angle is greater than 90 degrees

Perimeter of a Triangle

The perimeter of a polygon is the total length of its boundary and is measured as the sum of all sides. A triangle has three sides so its perimeter is the sum of all three sides.

Steps for Calculation of Perimeter of a Triangle

The steps used to calculate the perimeter of triangle are as follows:

1. The values of all three sides are noted along with their units.

2. The three values are added.

3. The sum obtained is the perimeter of the triangle.

For example, a triangle has three sides equal to 5 cm, 8 cm, and 10 cm. So the perimeter of this triangle will be, (5 + 8 + 10) cm = 23 cm

Different Types of Perimeter of Triangle

• Equilateral triangle
  This type of triangle has three equal sides. So the perimeter of an equilateral triangle will be 3 times the dimension of one side. If the sides of an equilateral triangle are ‘a’ unit then its perimeter will be (3 X a) units.

• Isosceles triangle
  An isosceles triangle has two equal sides and one unequal side. If each equal side is ‘p’ units and the third side is ‘q’ units, then the perimeter of the triangle will be (p + p + q) units = (2p + q) units.

• Right-angle triangle
  In this type of triangle, the square of the hypotenuse (largest side) is equal to the sum of the squares of the other two sides. So if the dimension of any two sides of a right-angle triangle is known, the other side can be calculated. Then by using values of all three sides, the perimeter is calculated.

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