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Types of Triangles
The different types of triangles are classified according to the length of their sides and as per the measure of the angles. The triangle is one of the most common shapes and is used in construction for its rigidity and stable shape. Understanding these properties allows us to apply the ideas in many real-world problems.
What are the Different Types of Triangles?
There are different types of triangles in math that can be distinguished based on their sides and angles.
The characteristics of a triangle’s sides and angles are used to classify them. The different types of triangles are as follows:
|Types of Triangle Based on Sides||Types of Triangles Based on Angles|
|Equilateral Triangle||Acute-Angled Triangle (Acute Triangle)|
|Isosceles Triangle||Right-Angled Triangle (Right Triangle)|
|Scalene Triangle||Obtuse-Angled Triangle (Obtuse Triangle)|
Types of Triangles Based on Sides
On the basis of side lengths, the triangles are classified into the following types:
A triangle is considered to be an equilateral triangle when all three sides have the same length.
When two sides of a triangle are equal or congruent, then it is called an isosceles triangle.
When none of the sides of a triangle are equal, it is called a scalene triangle.
Types of Triangles Based on Angles
On the basis of angles, triangles are classified into the following types:
- Acute Triangle: When all the angles of a triangle are acute, that is, they measure less than 90°, it is called an acute-angled triangle or acute triangle.
- Right Triangle: When one of the angles of a triangle is 90°, it is called a right-angled triangle or right triangle.
- Obtuse Triangle: When one of the angles of a triangle is an obtuse angle, that is, it measures greater than 90°, it is called an obtuse-angled triangle or obtuse triangle.
Types of Triangle Based on Sides and Angles
The different types of triangles are also classified according to their sides and angles as follows:
Equilateral or Equiangular Triangle:
When all sides and angles of a triangle are equal, it is called an equilateral or equiangular triangle.
Isosceles Right Triangle:
A triangle in which 2 sides are equal and one angle is 90° is called an isosceles right triangle. So, in an isosceles right triangle, two sides and two acute angles are congruent.
Obtuse Isosceles Triangle:
A triangle in which 2 sides are equal and one angle is an obtuse angle is called an obtuse isosceles triangle.
Acute Isosceles Triangle:
A triangle in which all 3 angles are acute angles and 2 sides measure the same is called an acute isosceles triangle.
Right Scalene Triangle:
A triangle in which any one of the angles is a right angle and all the 3 sides are unequal, is called a right scalene triangle.
Obtuse Scalene Triangle:
A triangle with an obtuse angle with sides of different measures is called an obtuse scalene triangle.
Acute Scalene Triangle:
A triangle that has 3 unequal sides and 3 acute angles is called an acute scalene triangle.
Here is a list of a few points that should be remembered while studying the types of triangles:
- In an equilateral triangle, each of the three internal angles is 60°.
- The three internal angles in a triangle always add up to 180°.
- All triangles have two acute angles.
- When all the sides and angles of a triangle are equal, it is called an equilateral or equiangular triangle.
☛ Related Topics:
- Construction of Triangles
- Similar Triangles
- Properties of Triangle
- Perimeter of Triangle
- Congruence in Triangles
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