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
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.
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.
We can classify triangles by the length of their sides.
All three sides have different lengths.
All three angles are different.
It has no lines of symmetry.
Has two equal sides.
The angles opposite the equal sides are also equal.
It has at least one line of symmetry.
All three sides are equal in length.
All three angles are equal (each angle = 60°).
It is the most symmetrical triangle.
Now, let’s explore triangle types by their internal angles.
All three angles are less than 90°.
It can be scalene, isosceles, or equilateral.
One angle is exactly 90°.
The side opposite the right angle is the hypotenuse.
Used in trigonometry and construction.
One angle is more than 90°.
It has only one obtuse angle because the total must stay 180°.
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.
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.
The 7 main types of triangles are:
Equilateral Triangle
Isosceles Triangle
Scalene Triangle
Acute Triangle
Right Triangle
Obtuse Triangle
Right Isosceles Triangle
These cover the main kinds of triangles by both sides and angles.
You can also make a longer list by combining side and angle classifications:
Equilateral - all sides and angles are equal
Isosceles Acute
Isosceles Right
Isosceles Obtuse
Scalene Acute
Scalene Right
Scalene Obtuse
Right Triangle
Acute Triangle
Obtuse Triangle
Right Isosceles Triangle
Acute Equilateral Triangle
Some triangles appear under more than one label.
Usually, people refer to these 4 triangle types:
Equilateral
Isosceles
Scalene
Right Triangle
These cover both triangle types by side and special angle.
You can classify triangle types in these ways:
By the number of equal sides
By the number of equal angles
By having a right angle
By having an obtuse angle
By having only acute angles
By symmetry
By pattern or purpose (like special triangles in geometry)
Each classification shows different triangle properties.
Here’s a full extended list combining types of triangles from all categories:
Equilateral Triangle
Isosceles Triangle
Scalene Triangle
Acute Triangle
Right Triangle
Obtuse Triangle
Right Isosceles Triangle
Right Scalene Triangle
Obtuse Isosceles Triangle
Obtuse Scalene Triangle
Acute Isosceles Triangle
Acute Scalene Triangle
Equiangular Triangle
Isosceles Right Triangle
Triangle with 30-60-90 angles
Triangle with 45-45-90 angles
Heron’s triangle
Golden triangle (based on the golden ratio)
Orthic triangle
Medial triangle
These advanced types are useful in higher-level mathematics.
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.
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.
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!
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.
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!
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!
Ans: The 7 common types of triangles are:
Equilateral
Isosceles
Scalene
Acute
Right
Obtuse
Right Isosceles
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
Ans: The 4 basic triangle types are:
Equilateral
Isosceles
Scalene
Right
Ans: You can classify triangles by:
Side length
Angle size
Equal sides
Right angles
Obtuse angles
Symmetry
Use or purpose in geometry
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!