A closed figure with three sides is a triangle.
Earlier we have learnt how the triangles are classified based on their sides.
Let us recall the types of triangle based on its sides:
(i) Equilateral triangle
(ii) Isosceles triangle
(iii) Scalene triangle
Now, let us explore how the triangles are classified based on their angles in detail.
The naming of triangles based on angles:
- Type - 1: Acute angled triangle
If all the three angles of the triangle are acute (less than \(90°\)), then it is called an acute angled triangle.
- Type - 2: Right angled triangle
If one of the angles of a triangle is right angle \((90°)\) and the other two are acute angles (less than \(90°\)), then its is called a right angled triangle.
- Type - 3: Obtuse angled triangle
If one of the angles of a triangle is an obtuse angle (greater than \(90°\)), and the other two are acute angle (less than \(90°\)), then it is called an obtuse angled triangle.
Angle Sum Property:
The sides of a triangle intersecting at a corner gives rise to an angle.
Let's see the remarkable property that connects three interior angles of a triangle.
Statement:
The sum of the measure of three angles of a triangle is \(180°\).
Consider a triangle \(ABC\) with interior angles measures \(∠A\), \(∠B\) and \(∠C\).
By the property, \(∠A + ∠B + ∠C = 180°\).
Enterior angle property:
The angle formed between the extension of one side of a triangle and its corresponding side is called an exterior angle of the triangle.
Statement:
An exterior angle of a triangle is equal to the sum of its opposite interior angles.
Consider a triangle \(ABC\), where side \(BC\) is extended to form an exterior angle at vertex \(C\). Then, the angles formed are, the interior angles \(\angle A\), \(\angle B\) and \(\angle C\), and the exterior angle at \(C\).
By the property, the exterior \(\angle C\) \(=\) \(\angle A\) \(+\) \(\angle B\).