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Types of Triangles – Definition & Examples

types of triangles

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A triangle is one of the basic shapes in geometry with three sides, three vertices, and three interior angles. There are basically six different types of triangles with respect to the length and measure of the lines and angles of a triangle, respectively.  

Let’s understand the six different types of triangles and their shapes and properties.

Types of Triangles

The triangles are broadly classified into two types:

  • Triangles based on the lengths of their sides
  • Triangles based on their interior angles

These two broad types of triangles are further classified as

Based on Their SidesBased on Their Angles
Equilateral TriangleAcute Triangle
Isosceles TriangleRight Triangle
Scalene TriangleObtuse Triangle
types of triangles
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Types of Triangles Based on Sides

Based on the length of the sides, triangles are classified into three types 

  • Equilateral Triangle
  • Isosceles Triangle
  • Scalene Triangle

Equilateral Triangle

In an equilateral triangle, all the lengths of the sides are equal. With respect to angles, each of the interior angles will have a measure of $60^{\circ}$. Since the angles of an equilateral triangle are the same, it is also known as an equiangular triangle.

types of triangles

In the above figure, $\triangle \text{ABC}$ is an equilateral triangle, where all three sides are equal i.e., $\text{AB} = \text{BC} = \text{CA}$ and measure of all the three angles is also equal and each equal to $60^{\circ}$.

Isosceles Triangle

In an isosceles triangle, the lengths of two of the three sides are equal. 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. 

types of triangles

In the above figure, $\triangle \text{PQR}$ is an isosceles triangle, where the two sides are equal i.e., $\text{PQ} = \text{PR}$ and the measure of two angles $\angle \text{PQR}$ and $\angle \text{QRP}$ are also equal.

Note: Angles opposite to equal sides are equal.

Scalene Triangle

In a scalene triangle, all side lengths are 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. 

types of triangles

In the above figure, $\triangle \text{LMN}$ is a scalene triangle, where all the three sides $\text{LM}$, $\text{MN}$, and $\text{NL}$ are of different lengths and all the three angles $\angle \text{LMN}$, $\angle \text{MNL}$, and $\angle \text{NLM}$ are unequal.

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Types of Triangles Based on Angles

Based on the interior angles, triangles are classified into three types 

  • Acute Triangle (or Acute-angled Triangle)
  • Right Triangle (or Right-angled Triangle)
  • Obtuse Triangle (or Obtuse-angled Triangle)

Acute Triangle

In an acute triangle, all three interior angles are acute. In other words, if the measure of all interior angles is less than $90^{\circ}$, then it is called an acute-angled triangle.

types of triangles

In the above figure, all the interior angles of the $\triangle {\text{LMN}}$ are less than $90^{\circ}$.

Right Triangle

In a right triangle, one of the angles is $90^{\circ}$ degrees. In a right-angled triangle, the side opposite to the right angle ($90^{\circ}$ angle) will be the longest side and is called the hypotenuse. The other two sides of the triangle are called the legs of the triangle (one of the sides is the base and the other is altitude or height).

Note: In a triangle, only one angle can be a right angle.

types of triangles

In the above figure, $\triangle \text{PQR}$ is a right triangle, where $\angle \text{PQR} = 90^{\circ}$. The side $\text{RP}$ is the longest side and is called hypotenuse and the sides $\text{PQ}$, and $\text{QR}$ are its legs ($\text{PQ}$ is the base and $\text{QR}$ is the height).

Obtuse Triangle

In an obtuse triangle, one of the three interior angles has a measure greater than $90^{\circ}$. In other words, if one of the angles in a triangle is an obtuse angle, then the triangle is called an obtuse-angled triangle. 

Note: In a triangle, only one angle can be an obtuse angle.

types of triangles

In the above figure, one of the angles i.e. $\angle \text{YZX}$ is more than $90^{\circ}$. Hence, it is an obtuse triangle.

Practice Problems

  1. What are the two broad classifications of triangles?
  2. What are the different types of triangles based on the length of the sides?
  3. What are the different types of triangles based on the measure of the angles?
  4. Define the following
    • Equilateral triangle
    • Isosceles triangle
    • Scalene triangle
    • Acute triangle
    • Right triangle
    • Obtuse triangle

FAQs

What are the types of triangles in Geometry?

There are six types of triangles in geometry. They can be classified into two groups. 
a) Based on their sides, there are three types of triangles –  equilateral triangles, isosceles triangles, and scalene triangles.
b) Based on their angles, there are three types of triangles – acute triangle, obtuse triangle, and right-angled triangle.

What are the three types of triangles based on their angles?

On the basis of angles, triangles are classified into an acute triangle, a right triangle, and an obtuse triangle.
a) Acute triangle: In an acute triangle, all the angles measure less than $90^{\circ}$.
b) Right Triangle: When one angle of a triangle measures $90^{\circ}$, it is called a right-angled triangle.
c) Obtuse Triangle: When one of the angles of a triangle is an obtuse angle, it is called an obtuse-angled triangle.

What are the three types of triangles based on sides?

On the basis of sides, triangles are classified into three types.
a) Equilateral triangle: When all three sides have the same length, the triangle is considered to be an equilateral triangle.
b) Isosceles triangle: If two sides of a triangle are equal, it is called an isosceles triangle.
c) Scalene triangle: If all the sides of a triangle are of different lengths, it is called a scalene triangle.

Conclusion

There are six types of triangles broadly classified into two categories – triangles based on sides and triangles based on angles. Based on sides the triangles can be equilateral, isosceles, or scalene, and based on angles, the triangles can be acute, right, or obtuse.

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