In this section, we will learn about basic properties of triangles and types of triangles.
Triangle is a closed polygon formed by three intersecting lines. A triangle consists of three sides, three vertices and three angles (As the name suggests “tri angle” means three angles).
Here, AB, BC and AC are the sides.
A, B and C are the three vertices.
∠A , ∠B and ∠C are the three angles.
PROPERTIES OF A TRIANGLE
Following are the basic properties of triangles.
- The sum of all the three angles of a triangle is always 180º .
- The sum of any two sides is always greater than the third side.
- In a triangle, the side opposite to the greater angle is longer.
- In a triangle, the angle opposite to the longer side is greater.
- Angles opposite to equal sides of a triangle are equal.
- Sides opposite to equal angles of a triangle are equal.
- When a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
- The sum of all the sides of a triangle is called its perimeter.Perimeter = sum of all sides = a + b + c
And half of the perimeter is called semi-perimeter.(s)
s = ( a + b + c )/ 2 - Area of a triangle = \frac{1}{2} x Base x Height
- By Heron’s Formula,
Area of a triangle = \sqrt{s(s-a)(s-b)(s-c)}
TYPES OF TRIANLGES
Triangles can be classified on the following basis –
On the basis of sides
- Scalene triangle
- Isosceles triangle
- Equilateral triangle
On the basis of angles
- Acute angled triangle
- Obtuse angled triangle
- Right angled triangle
Types of triangles on the basis of sides
There are three types of triangles-
a) Scalene triangle – When in a triangle the length of each side is different from another, it is called scalene triangle.
b) Isosceles triangle – When in a triangle, the length of any two sides are equal, then it is called isosceles triangle.
c) Equilateral triangle – When in a triangle the length of all sides are equal then it is called equilateral triangle.
Area and perimeter of different triangles can be given by-
Types of triangles on the basis of angles
- Acute angled triangle – In a triangle when all the angles are acute angles , then the triangle is called acute angled triangle.
- Obtuse angled triangle – In a triangle when one angle is obtuse angle, then the triangle is called obtuse angled triangle.
- Right angled triangle – When one angle of a triangle is 90º, then the triangle is called right angled triangle.
In a right angled triangle the side opposite to the 90º angle is the greatest and is called HYPOTENUSE.
Also,
(BC)^{2} = (AC)^{2} + (AB)^{2}
This is called the Pythagoras theorem.
It states that, In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.
i.e.
(Hypotenuse)^{2} = sum of the squares of the other two sides.
You may also want to learn the following for more clear concepts.