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There are three sides in a triangle. Let us know more about the triangles in this article.

A triangle is a two-dimensional closed polygon and has three sides. Each of the three sides of a triangle is made of straight lines. Each side made of a straight line intersects with another side to form a vertex. The three vertices formed in a triangle are non-collinear points, which means they do not lie on the same straight line. An angle is formed between two sides intersecting each other at a vertex of a triangle. Hence, any triangle will have three sides, three vertices, and three angles. Triangles make up a very important part of geometry. Read further to know more about triangles.

A triangle can be described in geometry as a three-sided polygon. A polygon is a flat structure that is two-dimensional and is bounded by straight lines. The number of lines also referred to as “sides” or “edges” in a polygon determines its type. For example, a four-sided polygon is called a “square” and a six-sided polygon is called a “hexagon”. Similarly, a three-sided polygon is called a “triangle”. The word “triangle” is derived from the Old Latin word “triangulus” from the Latin word “tres” or “tri-” meaning three and “angulus” meaning corner or angle.

It is important to know the various parts of a triangle to have a thorough understanding of the shape. A triangle has three main parts that we need to be familiar with. These are - side, vertex, and angle. We can denote the various parts of an angle using their common representation.

A triangle is commonly denoted by the alphabetical representation of its vertices. For example, if the three vertices of a triangle are named A, B, and C respectively, the triangle will be denoted as ABC.

The three sides of the triangle in this case would be side AB, side BC, and side CA.

Side AB and side BC intersect at vertex B to form angle ABC.

Side BC and side CA intersect at vertex C to form angle BCA.

Side CA and side AB intersect at vertex A to form angle CAB.

Triangles have some important properties that define them. These are:

The sum of the interior angles of any triangle should be equal to 180 degrees. Interior angles are those angles that lie inside a polygon. Hence, for a triangle, the angles that lie inside the shape and are created by the sides during the intersection at the vertices, are called interior angles. This is a fundamental property of a triangle. If the sum of the interior angles of a polygon does not add up to 180 degrees, we can say without a doubt that the shape is not a triangle.

Any two sides of a triangle have lengths that, when added together, are more than the length of the third side. Similarly, the length difference between any two sides of a triangle is lesser than the length of the third side.

The side of the triangle that is shortest in length will always be right opposite to the smallest interior angle. The side of the triangle that is the longest in length will always be right opposite to the largest interior angle.

For example, a triangle has three angles measuring 30 degrees, 60 degrees, and 90 degrees. Using this property we can say that the side that is opposite to the angle of 30 degrees is the smallest side in length, and the side opposite to the angle of 90 degrees is the longest side in length.

Triangles can be classified into different types on the basis of the length of their sides and on the basis of the measurement of angles.

Types of triangles based on the length of their sides:

**Equilateral Triangles**

A triangle that has all three sides of the same length is called an equilateral triangle. As each of the sides are of the same length, the internal angles too are of the same measurement. We know that the sum of all internal angles of a triangle adds up to 180 degrees. Hence, in an equilateral triangle, each of the three interior angles is 60 degrees.

**Isosceles Triangles**

An isosceles triangle has two of its three sides of similar length. The interior angles opposite to the two equal sides are also equal in measurement.

**Scalene Triangles**

A triangle that has all three sides of different lengths is called a scalene triangle. The interior angles of a scalene triangle are also different in measurement.

Types of triangles based on the measurement of their interior angles:

**Acute Triangle**

If all the angles of a triangle are less than 90 degrees, it is called an acute triangle.

For example, a triangle ABC has interior angles measuring 50 degrees, 60 degrees, and 70 degrees respectively. As all three angles are less than 90 degrees, triangle ABC is an acute triangle.

**Right Angle Triangle**

If a triangle has one angle that is exactly 90 degrees, it is called a right-angle triangle.

For example, a triangle DEF has interior angles measuring 30 degrees, 60 degrees, and 90 degrees respectively. This triangle DEF is a right-angle triangle.

**Obtuse Triangle**

If a triangle has one angle that measures more than 90 degrees, it is called an obtuse triangle.

For example, a triangle XYZ has interior angles measuring 30 degrees, 40 degrees, and 110 degrees respectively. This triangle XYZ is an obtuse angled triangle.

The perimeter of a triangle is the total length of the shape’s boundary. The perimeter of any triangle is the sum of the length of its three sides.

An equilateral triangle has equal sides and equal angles with each angle measuring 60 degrees. All three angles of an acute triangle measure less than 90 degrees. Because 60 degrees is lesser than 90 degrees, we can say that all equilateral triangles are acute triangles.

The area of a triangle can be calculated if we know the length of the base and the length of the height of the triangle. The formula for calculating the area of a triangle is as follows:

\begin{equation}

\text { Area }=1 / 2 \times \text { Base } \times \text { Height }

\end{equation}

When one of the sides of a triangle is extended, the angle it makes with its adjoining side is known as the external angle of a triangle. For example, in triangle ABC

A triangle ABC has sides with length AB = 4cm, BC = 4cm, and CA= 7cm. What type of triangle is it?

The triangle ABC is an isosceles triangle. This is because two out of the three sides of the triangle are equal in length. Side AB and side BC both are 4cm long, and hence triangle ABC is an isosceles triangle.

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