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.
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.
5th Grade Geometry Page
5th Grade Math Problems
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