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Classification of triangles is done according to the length of their sides and the measure of the angles. A triangle is a simple polygon with 3 sides, 3 interior angles, and 3 vertices that are joined with each other and it is denoted by the symbol △. This is the most common shape seen in math and nature and is of various types. In this article, classifying triangles is seen in detail along with a few solved examples to understand the concept better.
|1.||Classification of Triangles|
|2.||Classification of Triangles Based on Sides|
|3.||Classification of Triangles Based on Angles|
|4.||Classification of Triangles Based on Angles and Sides|
|5.||FAQs on Classifying Triangles|
Classification of Triangles
Classification of triangles is done based on their sides and angles. In other words, the characteristics of a triangle's size and shape help in distinguishing the type of triangle. The table below shows the different types of triangles based on their angles and sides.
|Based on Sides||Based on Angles||Based on Sides & Angles|
|Equilateral Triangle||Acute Angle||Equiangular Triangle|
|Isosceles Triangle||Obtuse Angle||Isosceles Right Triangle|
|Scalene Triangle||Right Angle||Obtuse Isosceles Triangle|
|Acute Isosceles Triangle|
|Right Scalene Triangle|
|Obtuse Scalene Triangle|
|Acute Scalene Triangle|
Let us see each type in detail.
Classification of Triangles Based on Sides
A triangle consists of three sides but the factor to classify them is the length of the sides. It is specifically based on the ratio of the lengths of the sides with one another rather than the unit measure. Hence, triangles are classified on the number of sides with the same length equal to each other or not equal at all. The three types of triangles are equilateral triangle, scalene triangle, and isosceles triangle.
Equilateral triangle is the most common type used while learning the basics of the shape. Here, the three sides are equal to each other along with the three angles measuring 60°. An equilateral triangle is considered a regular polygon with angles and sides equal.
The word isosceles is derived from the Greek word 'iso' which means same and 'skelos' which means leg. This type of triangle has two sides of the same length. The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.
A scalene triangle is a triangle with all three sides of different lengths along with three angles of different measures. This shape does not have a line of symmetry i.e. no matter where a line is drawn through a scalene triangle, the left and right sides of the line will never be equal to each other.
Classification of Triangles Based on Angles
Triangles can also be classified on the basis of angles. All triangles have three interior angles whose angle measurements sum to 180° with different combinations of angles depending on the type of triangle. The three different types are acute triangle, obtuse triangle, and right triangle.
Acute triangle is a type of triangle where all three interior angles are acute angles or less than 90°. The sides of an acute-angled triangle can be equal or unequal depending on whether the triangle is equilateral, isosceles, or scalene.
A right-angled triangle is a triangle with one of the angles as 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle. Here, the relationship between the sides is understood with the help of the Pythagoras rule. The side opposite to the right angle is the largest side and is referred to as the hypotenuse.
An obtuse-angled triangle or obtuse triangle is a type of triangle whose one of the vertex angles is bigger than 90° and the sum of the other two angles is less than 90°. The side opposite to the obtuse angle is considered the longest.
Classification of Triangles Based on Angles and Sides
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.
☛ Related Topics
Listed below are a few topics related to classifying triangles, take a look!
Classifying Triangles Example
Example 1: Which of the following angle measures can form an obtuse-angled triangle?
a) 60°, 70°, 50°
b) 95°, 30°, 55°
c) 89°, 45°, 46°
d) 90°, 60°, 30°
An obtuse-angled triangle has one of the vertex angles as an obtuse angle (> 90°). Among the given options, option (b) satisfies the condition. Therefore, option b i.e. 95°, 30°, 55° forms an obtuse triangle.
Example 2: The length of the three sides of a triangle is not equal. Identify the type of triangle.
In a scalene triangle, the length of the three sides is not equal. Therefore, the given triangle can be identified as a scalene triangle.
Example 3: If each vertex angle of a triangle measures 60°, identify the type of triangle based on triangle properties.
It is given that all the interior angles of the given triangle measure 60° each. We know that all the angles in an equilateral triangle measure the same and they sum up to 180°, hence, each angle measures 60°. Therefore, the given triangle is an equilateral triangle.
FAQs on Classifying Triangles
What is the Classification of Triangles in Geometry?
Triangles are classified according to 2 groups i.e. sides and angles and are of six types in total. 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.
What are the 3 Triangles Classified 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 Triangles Classified 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.
What 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.
What Triangles Have a 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.
What is the Difference Between Equilateral and Equiangular Triangle?
Both the triangles are considered as regular polygons. The main difference between the two triangles is that an equilateral triangle or polygon has congruent sides like a rhombus whereas an equiangular triangle or polygon has congruent interior angles like a rectangle. If a polygon is both equilateral and equiangular, it is considered a regular polygon.