Sunday, May 3, 2020

Triangle (Properties of Triangles)

In this video I will teach you Mathematics topic Triangle.

This is most important topic Triangle.Please watch and write comments.
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Introduction


You have studied about triangles and their various properties in your earlier classes. You know that a closed figure formed by three intersecting lines is called a triangle. (‘Tri’ means ‘three’). A triangle has three sides, three angles and three vertices. For example, in triangle ABC, denoted as Δ ABC (see Fig. 7.1); AB, BC, CA are the three sides, ∠ A, ∠ B, ∠ C are the three angles and A, B, C are three vertices. In Chapter 6, you have also studied some properties of triangles. In this chapter, you will study in details about the congruence of triangles, rules of congruence, some more properties of triangles and inequalities in a triangle. You have already verified most of these properties in earlier classes. We will now prove some of them.


Following are the basic properties of triangles:

  1. The sum of all internal angles of a triangle is always equal to 1800. This is called the angle sum property of a triangle.
  2. The sum of the length of any two sides of a triangle is greater than the length of the third side.
  3. The side opposite to the largest angle of a triangle is the largest side.
  4. Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.
  5. https://www.youtube.com/watch?v=5xSyHdGcc7Y&t=23s


Scalene Triangle

scalene triangle has all side lengths of different measures. No side will be equal in length to any of the other sides in such a triangle. In a scalene triangle, all the interior angles are also different. The figure given below illustrates a scalene triangle. You can see how none of the sides is equal in length.

Isosceles Triangle

In an isosceles triangle, the lengths of two of the three sides are equal. So, the angles opposite the equal sides are equal to each other. In other words, an isosceles triangle has two equal sides and two equal angles.  The figure given below illustrates an isosceles triangle.

Equilateral Triangle

In an equilateral triangle, all the lengths of the sides are equal. In such a case, each of the interior angles will have a measure of 60 degrees. Since the angles of an equilateral triangle are same, it is also known as an equiangular triangle. The figure given below illustrates an equilateral triangle.



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