# Triangle

Triangle is one of the basic shape in geometry.

A triangle is a simple closed figure made up of three line segments. It has three sides and three vertices. It is represented by the symbol

We know that we can mark many points on any given line.

Three or more points which lie on the same line are called collinear points.

Above, points A, B, C and D which lie on the same line collinear points.

But in the figure below, only two points A and D lied on the line. Points B, E, C and F do not lie on that line.

Hence, these points A, B, C, D, E, F are called non - collinear points.

If we join three non - collinear points L, M and N lie on the plane of paper, then we will get a closed figure bounded by three line segments LM, MN and NL. This closed figure is called a Triangle.

The three line segments of a triangle are also known as sides of the triangle.

This triangle is named as ∆ LMN with its side as LM, MN and NL and three vertices as L, M and N.

The three angles named as ∠ LMN, ∠MNL and ∠ NLM are the angles of the triangle.

Three angles are denoted by ∠M, ∠N and ∠L respectively.

The three angles and the three sides of a triangle are together called the six parts or elements of the triangle.

Thus, a closed figure bounded by three line segments is called a triangle.

is the symbol to denote a triangle.

Note: A triangle has 6 elements: Three sides and three angles.

Thus 1. A triangle is named in three different ways

(i) ∆LMN or (ii) ∆MNL or (iii) ∆NLM

2. Vertices of ∆LMN are L, M, N.

3. Angles of ∆LMN are ∠L, ∠M and ∠N.

4. Line segments of ∆LMN are LM, MN, NL.

The side LM is the base of the ∆ NLM. ∠N opposite to the base LM is called the Vertical angle of the triangle.

∠N and ∠M adjacent to the base LM are called Base angles.

If we add up the three sides of a triangle, we get its perimeter.

Thus the perimeter of the ∆LMN = LM + MN + NL.

Note: Therefore, a triangle has:

Three line segments,

Three vertices,

Three angles.

Classification of Triangle.

Properties of Triangle.

Worksheet on Triangle.

To Construct a Triangle whose Three Sides are given.

To Construct a Triangle when Two of its Sides and the included Angles are given.

To Construct a Triangle when Two of its Angles and the included Side are given.

To Construct a Right Triangle when its Hypotenuse and One Side are given.

Worksheet on Construction of Triangles.

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