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.

Classifying Triangles

The characteristics of a triangle’s sides and angles are used to classify them. The different types of triangles are as follows:

On the basis of side lengths, the triangles are classified into the following types:

• Equilateral Triangle: A triangle is considered to be an equilateral triangle when all three sides have the same length.
• Isosceles triangle: When two sides of a triangle are equal or congruent, then it is called an isosceles triangle.
• Scalene triangle: When none of the sides of a triangle are equal, it is called a scalene triangle.

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.

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.

☛Important Notes:

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

What are the Types of Triangles in Geometry?

There are six types of triangles in geometry. They can be classified according to 2 groups. Based on their sides, the 3 triangles are classified as equilateral triangles, isosceles triangles, and scalene triangles. Based on their angles, the 3 types of triangles are listed as, acute triangle, obtuse triangle, and right-angled triangle. Thus, there are six types of triangles in geometry.

What are the 3 Types of Triangles Based on their Angles?

On the basis of angles, triangles are classified into acute triangle, right triangle, and obtuse triangle.

• Acute triangle: In an acute triangle, all the angles measure less than 90°.
• Right Triangle: When one angle of a triangle measures 90°, it is called a right-angled triangle.
• Obtuse Triangle: When one of the angles of a triangle is an obtuse angle, it is called an obtuse-angled triangle.

What are the Types of Triangles Based on Sides?

On the basis of sides, triangles are classified into 3 types.

• Equilateral triangle: When all three sides have the same length, the triangle is considered to be an equilateral triangle.
• Isosceles triangle: If two sides of a triangle are equal, it is called an isosceles triangle.
• Scalene triangle: If all the sides of a triangle are of different lengths, it is called a scalene triangle.

Which Types of Triangles Have 3 Lines of Symmetry?

All equilateral triangles have 3 lines of symmetry as three lines of symmetry can pass through the vertex of this triangle.

Which Types of Triangles Have Reflection Symmetry?

All equilateral and isosceles triangles have reflection symmetry.

What are the 6 Types of triangles?

The 6 types of triangles can be listed as, acute triangle, obtuse triangle, right triangle, equilateral triangle, isosceles triangle, and scalene triangle.