Triangle: Definition, Types | Formula | Solved Examples

Triangle: Triangle is a polygon consisting of three sides and three vertices. It is considered to be one of the most important geometrical shapes. There are three types of triangles – equilateral, isosceles and scalene based on the length of the sides. Also, triangles are categorized based on the measurement of angles – acute, right and obtuse. The sum of the internal angles of a triangle is equal to 180 degrees. If ABC is a triangle, then it will be denoted as ∆ABC.

Students learn different types of shapes from an early age in order to solve mathematical problems such as Pythagoras theorem and trigonometry in fractions of seconds. To understand the concepts of triangles better, you can download NCERT Solutions for Class 7 Maths Chapter 6 – Triangle And Its Properties. We have provided detailed information on Triangle in this article. Read on to find out about its definition, types, properties, formulas and few solved examples.

Triangle: Definition

Triangle is a two-dimensional polygon with three sides. Any two sides are joint by a vertex. Therefore, it has three vertices. And, there is an angle formed between the two sides of the triangle.

Angles of Triangle:

There are three angles formed in a triangle. Each angle is formed by two sides of the triangle at the fixed point known as vertex. The sum of all three angles will be equal to 180 degrees.

Triangle: Types

Triangles are classified based on the length of the sides and the measurement of the angles.

On the basis of length, there are three types of triangle i.e., Scalene, Isosceles and Equilateral. They are as follows:

Scalene Triangle: The three sides of a scalene triangle have different lengths.

Isosceles Triangle: This type of triangle has two equal sides and one different. Due to this, the angles opposite to the sides are equal to each other.

Equilateral Triangle: This type of triangle has all three sides equal to each other. Due to this, each angle of an equilateral triangle measures 60 degree.

On the basis of measurement of angles, there are three types of angles – Acute, Right and Obtuse.

Acute Triangle: If all the three internal angles of a triangle measure less than 90°, then it is an acute-angled triangle. The three internal angles are called acute angles.

Right Triangle: If any one of the internal angles of a triangle measures 90°, it is a right-angled triangle

Obtuse Triangle: If one of the three sides of a triangle measure more than 90°, then it is an obtuse-angled triangle.

Triangle: Properties

All geometrical shapes possess some properties that distinguish them from others. Here are some of the properties of triangle:

1. A triangle has three sides.
2. A triangle has three vertices.
3. The sum of consecutive interior and exterior angle is supplementary.
4. The shortest side is always opposite to the smallest angle of the triangle.
5. The sum of three interior angles of a triangle is 180 degrees.
6. The perimeter is equal to the sum of all three sides of a triangle.
7. The area of a triangle is equal to half of base multiplied by height.

Triangle: Formulas

Check the following formulas used to measure the perimeter and area of a triangle:

A perimeter is the total length of the outer boundary of the triangle. We can say that perimeter is equal to the sum of all three sides.

If ABC is a triangle, then AB, BC, and AC are the length of the sides. Therefore, perimeter of the triangle ABC is equal to AB +BC+AC.

Area is the space occupied by the triangle in the two-dimensional plane. Area is equal to the half of base multiplied by height.

Triangle: Solved Examples

Go through the following solved examples of triangle:

Example 1: If triangle ABC has AB= 5 cm, BC= 6 cm and AC = 4 cm sides. Find the perimeter of the triangle

Solution: Given ABC is a triangle

AB= 5 cm, BC= 6 cm and AC = 4 cm

Perimeter= 5+6+4 = 15 cm

Example 2: Find the area of a triangle with base 9 cm and height 5 cm.

Solution: Given, Base= 9 cm , height= 5 cm

Area = 1/2 base x height

= 1/2 x 9 x 5

= 22.5 cm

FAQs Regarding Triangle

The frequently asked questions on triangle are given below:

We have now provided you with a detailed article on Triangle. Make the best use of it and refer to the provided if you face any difficulty while solving the NCERT exercise questions.

We hope this article on Triangle helps you. If you have any question, feel to post it in the comment box below. We will get back to you at the earliest.