Types of Triangles
All triangles have three sides and three angles, but they come in many different sizes and shapes. Triangles can be categorized by various properties based on their angles and sides, and understanding these properties allows you to apply the ideas in many real-world problems. The triangle is one of the strongest shapes and hence it is used in construction for its rigidity and stable shape.
|1.||Types of Triangles and Their Classification|
|2.||Types of Triangles Based on Side Length|
|3.||Types of Triangles Based on Angles|
|4.||Types of Triangle Based on Sides and Angles|
Types of Triangles and Their Classification
There are different types of triangles in math based on their sides and angles.
Types of Triangles
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 Side Length
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.
Types of Triangles Based on Angles
On the basis of angles, the triangles are classified into the following types:
- Acute Triangle: When all the angles of a triangle are acute, they measure less than 90°, it is called an acute-angled triangle or acute triangle.
- Right Triangle: When one of the angles of the 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, measure greater than 90°, it is called an obtuse-angled triangle or obtuse triangle.
Types of Triangle Based on Sides and Angles
We classify the triangles further based on 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 all 3 acute angles is called an acute scalene triangle.
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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 are supplementary, always add up to 180°
- All triangles have two acute angles
- When all sides and angles of a triangle are equal, it is called an equilateral or equiangular triangle.
Solved Examples on Types of Triangles
Example 1: What will be the measure of each angle in an equilateral triangle? Choose the right answer from one of the options
a) 30° b) 45° c) 60° d) 80°
All the interior angles are equal in an equilateral triangle. The sum of all the three angles should be 180° in a triangle. Therefore, each side measures 60°.
Example 2: The length of the two sides of a triangle is equal. Identify the type of triangle.
(a) Equilateral triangle (b) Scalene triangle (c) Isosceles triangle (d) Acute angled triangle
(a) A triangle is considered to be equilateral when all three sides have the same length. In a scalene triangle, the length of none of the sides of the triangle will be equal.
(b) In an isosceles triangle, the length of the two sides of the triangle will be equal.
(c) Acute angled triangle is a classification based on angles.
(d) Since the length of the two sides in this triangle are equal, the given triangle can be identified as an isosceles triangle.
FAQs on Types of Triangles
How Many Types of Triangles Are there in Geometry?
There are six types of triangles in geometry. Initially, there were 3 types based on their sides. But the geometry experts weren’t satisfied with just these three types of triangles. So, they also decided to classify triangles based upon the type of angles inside the triangle. Hence, there are three types of triangles based on angles. Thus, there are six types of triangles in geometry.
What Are the Types of Triangles Based on their Angles?
On the basis of angles, triangles are classified into the following 3 types: acute triangle, right triangle, and obtuse triangle.
What Are the Types of Triangles Based on Sides?
On the basis of sides, triangles are classified into the following 3 types: equilateral triangle, isosceles triangle, and 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.