Orchids Logo

Types of Triangles

Triangles are one of the key shapes in geometry. A triangle is a closed figure made of three straight lines that create three angles. Although triangles appear simple, they have many interesting types and properties used in real life, math, engineering, and art. 

In this blog, we will explore the different types of triangles, learn the main properties of triangles, and understand how to classify triangles based on their sides and angles. You’ll also find formulas, facts, real-life uses, and answers to common questions about triangle types.

 

Table of Contents

 

What Is a Triangle?

A triangle is a 3-sided polygon. It has:

  • Three sides

  • Three corners (vertices)

  • Three angles

The total sum of all internal angles in a triangle is always 180°. This is one of the most important properties of triangles.

 

Why Learn About Triangles?

Understanding types of triangles is useful because:

  • It helps in solving geometry problems in school.

  • Engineers and architects use triangles in building structures.

  • Triangles are used in maps, bridges, art, and even computer graphics.

  • Knowing triangle properties improves logical and spatial thinking.

 

Types of Triangles Based on Sides

We can classify triangles by the length of their sides.

Scalene Triangle

  • All three sides have different lengths.

  • All three angles are different.

  • It has no lines of symmetry.

Isosceles Triangle

  • Has two equal sides.

  • The angles opposite the equal sides are also equal.

  • It has at least one line of symmetry.

Equilateral Triangle

  • All three sides are equal in length.

  • All three angles are equal (each angle = 60°).

  • It is the most symmetrical triangle.

Types of Triangles Based on Angles

Now, let’s explore triangle types by their internal angles.

Acute Triangle

  • All three angles are less than 90°.

  • It can be scalene, isosceles, or equilateral.

Right Triangle

  • One angle is exactly 90°.

  • The side opposite the right angle is the hypotenuse.

  • Used in trigonometry and construction.

Obtuse Triangle

  • One angle is more than 90°.

  • It has only one obtuse angle because the total must stay 180°.

Combination of Classifications

Some triangles can fit into more than one category.

For example:

  • A right isosceles triangle has one 90° angle and two equal sides.

  • An acute scalene triangle has three unequal sides and all angles less than 90°.

  • An obtuse isosceles triangle has one angle more than 90° and two equal sides.

This overlap shows that kinds of triangle can be grouped in more than one way.

 

Triangle Properties

Let’s look at some key triangle properties that apply to all types of triangles:

  • Sum of interior angles = 180°

  • Exterior angle = sum of two opposite interior angles

  • Triangle inequality: The sum of any two sides is always greater than the third side

  • Area of triangle = ½ × base × height

  • Equilateral triangles have the same side lengths and angle measures

  • The Pythagorean theorem applies to right-angled triangles:
    a2+b2=c2a^2 + b^2 = c^2a2+b2=c2

These properties of triangles help in calculations and problem-solving.

 

What Are the 7 Types of Triangles?

The 7 main types of triangles are:

  1. Equilateral Triangle

  2. Isosceles Triangle

  3. Scalene Triangle

  4. Acute Triangle

  5. Right Triangle

  6. Obtuse Triangle

  7. Right Isosceles Triangle

These cover the main kinds of triangles by both sides and angles.

 

What Are the 12 Types of Triangles and Their Classifications?

You can also make a longer list by combining side and angle classifications:

  1. Equilateral - all sides and angles are equal

  2. Isosceles Acute

  3. Isosceles Right

  4. Isosceles Obtuse

  5. Scalene Acute

  6. Scalene Right

  7. Scalene Obtuse

  8. Right Triangle

  9. Acute Triangle

  10. Obtuse Triangle

  11. Right Isosceles Triangle

  12. Acute Equilateral Triangle

Some triangles appear under more than one label.

 

What Are the 4 Types of Triangles?

Usually, people refer to these 4 triangle types:

  1. Equilateral

  2. Isosceles

  3. Scalene

  4. Right Triangle

These cover both triangle types by side and special angle.

 

What Are the 7 Ways to Classify Triangles?

You can classify triangle types in these ways:

  1. By the number of equal sides

  2. By the number of equal angles

  3. By having a right angle

  4. By having an obtuse angle

  5. By having only acute angles

  6. By symmetry

  7. By pattern or purpose (like special triangles in geometry)

Each classification shows different triangle properties.

 

What Are the 20 Types of Triangles and Their Names?

Here’s a full extended list combining types of triangles from all categories:

  1. Equilateral Triangle

  2. Isosceles Triangle

  3. Scalene Triangle

  4. Acute Triangle

  5. Right Triangle

  6. Obtuse Triangle

  7. Right Isosceles Triangle

  8. Right Scalene Triangle

  9. Obtuse Isosceles Triangle

  10. Obtuse Scalene Triangle

  11. Acute Isosceles Triangle

  12. Acute Scalene Triangle

  13. Equiangular Triangle

  14. Isosceles Right Triangle

  15. Triangle with 30-60-90 angles

  16. Triangle with 45-45-90 angles

  17. Heron’s triangle

  18. Golden triangle (based on the golden ratio)

  19. Orthic triangle

  20. Medial triangle

These advanced types are useful in higher-level mathematics.

 

Real-Life Examples of Triangles

Triangles are used everywhere!

  • Architecture: Triangular shapes in bridges and roofs

  • Art and Design: Triangle patterns in drawings

  • Technology: Triangles in computer graphics

  • Math and Science: Triangles in trigonometry, physics, and geometry

  • Nature: Some mountains and crystals form triangle shapes

That’s why understanding the kinds of triangles is so helpful.

 

Practice Questions

  • Name a triangle with two equal sides and one 90° angle.

  • Find the missing angle in a triangle with 40° and 75°.

  • Classify a triangle with sides 6 cm, 6 cm, and 4 cm.

  • What is the area of a triangle with base 10 cm and height 6 cm?

  • Identify the type of triangle formed by angles 60°, 60°, and 60°.

Practising with such problems helps reinforce the triangle properties.

 

Common Mistakes Students Make

  • Thinking equilateral and isosceles are the same

  • Forgetting the angle sum must be 180°

  • Mislabeling triangle types based on sides only

  • Using the wrong height when finding area

  • Not using the Pythagorean theorem for right triangles

Remember to check the triangle rules carefully!

 

Tips and Tricks

  • Always add angles to confirm they total 180°

  • Use a ruler and protractor to check sides and angles

  • Remember: equal sides = equal angles

  • Use formulas for area and perimeter depending on what’s given

  • Draw triangles and label sides/angles clearly

Knowing the core triangle properties makes everything easier.

 

Fun Facts

  • The triangle is the strongest shape used in construction

  • The Pythagorean Theorem only works for right-angled triangles

  • A triangle with all angles less than 60° is impossible

  • The Eiffel Tower uses many triangle structures

  • Triangles are used in traffic signs for safety!

Conclusion

Triangles are not just three-sided shapes; they play a key role in geometry, art, and engineering. By understanding the different types of triangles, we can solve problems, spot patterns, and create better structures. Whether you encounter triangle types in tests or everyday life, knowing their properties makes math more meaningful and enjoyable. So the next time you see a triangle in a drawing or on a bridge, you'll know exactly what kind it is!

 

Related Topics 

Pythagoras Theorem - Unlock the Power of Right Triangles! Learn and apply the Pythagoras Theorem with easy steps, real-life examples, and fun problems.

Point and Lines - Get to the Point (and Line)! Discover how points and lines form the basics of geometry. Learn through visuals and simple definitions!

Two-Dimensional Shapes - Shape Up Your Knowledge! Explore 2D shapes like squares, circles, and triangles with clear explanations and everyday examples. Perfect for all learners!

 

Frequently Asked Questions on Types of Triangles

1. What are the 7 types of triangles?

Ans: The 7 common types of triangles are:

  1. Equilateral

  2. Isosceles

  3. Scalene

  4. Acute

  5. Right

  6. Obtuse

  7. Right Isosceles

 

2. What has 12 sides and 12 angles?

Ans: A shape that has 12 sides and 12 angles is called a dodecagon. In geometry, a dodecagon is a polygon with twelve straight sides and twelve interior angles. If all sides and angles are equal, it is called a regular dodecagon

 

3. What are the 4 types of triangles?

Ans: The 4 basic triangle types are:

  1. Equilateral

  2. Isosceles

  3. Scalene

  4. Right

 

4. What are the 7 different ways you can classify triangles?

Ans: You can classify triangles by:

  • Side length

  • Angle size

  • Equal sides

  • Right angles

  • Obtuse angles

  • Symmetry

  • Use or purpose in geometry

 

5. What type of triangle is ABC?

Ans: If all three sides of triangle ABC are equal, it is an Equilateral Triangle.

If two sides are equal, it is an Isosceles Triangle.

If all sides are different, it is a Scalene Triangle.

If one angle is 90°, it is a Right Triangle.

If all angles are less than 90°, it is an Acute Triangle.

If one angle is more than 90°, it is an Obtuse Triangle.

 

Explore more exciting math concepts with Orchids The International School!

Share
Loading Footer...