Types of Triangles Explained: Sides, Angles & Examples

The concept of types of triangles plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios.

What Is Types of Triangles?

A triangle is a closed, two-dimensional shape formed by three straight lines. There are several types of triangles based on the length of their sides and the measures of their angles. This classification is essential for understanding geometry, finding area or perimeter, and solving many mathematics problems.
You’ll find this concept applied in areas such as coordinate geometry, trigonometry, and even architecture.

Types of Triangles in Maths

Triangles can be classified in two main ways:

• By their sides: equilateral, isosceles, and scalene
• By their angles: acute, right, and obtuse

The following table summarises all the types of triangles:

Type	Based On	Description	Key Properties
Equilateral	Sides	All sides and angles are equal (each angle = 60°)	3 axes of symmetry; area = \( \frac{\sqrt{3}}{4}a^2 \)
Isosceles	Sides	Two sides and two angles are equal	Base angles equal; can be acute, right, or obtuse
Scalene	Sides	All sides and angles are different	No symmetry; area by Heron’s formula
Acute	Angles	All angles are less than 90°	Can be equilateral, isosceles, or scalene
Right	Angles	One angle is exactly 90°	Follows Pythagoras Theorem; area = ½ × base × height
Obtuse	Angles	One angle greater than 90°	Other two angles acute; sum is 180°

Key Formula for Types of Triangles

Here are the standard area formulas for different types of triangles:

• Equilateral: \( \text{Area} = \frac{\sqrt{3}}{4}a^2 \) (where a = side)
• Isosceles & Right: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \)
• Scalene: Heron’s formula \( \text{Area} = \sqrt{s(s-a)(s-b)(s-c)} \) where \( s = \frac{a+b+c}{2} \)

Step-by-Step Illustration

Let’s classify a triangle with sides 5 cm, 5 cm, and 8 cm:

1. Check the lengths: Two sides are equal (5 cm)

2. The angle opposite the longest side will be the largest; compute if the triangle is right, acute, or obtuse (using Pythagoras if required)

3. Since two sides are equal, it is an isosceles triangle.

4. Now check the square of the longest side (8² = 64) and sum of squares of other two (5² + 5² = 50); since 64 > 50, angle is obtuse.

5. So, it is an **isosceles and obtuse** triangle.

Speed Trick or Memory Hack

• All equilateral triangles are always acute-angled.
• Scalene triangles have all unequal sides and all unequal angles.
• Any triangle can have at most one obtuse or one right angle.

Vedantu’s live classes use charts and color-coded diagrams to help you remember these quickly for exams.

Try These Yourself

• Can a triangle have two obtuse angles? Why or why not?
• Identify the type of triangle with angles 70°, 60°, and 50°.
• Classify a triangle with sides 7 cm, 9 cm, and 13 cm.
• Which type of triangle is used in traffic signboards?

Frequent Errors and Misunderstandings

• Mixing up 'isosceles' with 'scalene'. Remember: isosceles has two equal sides.
• Thinking an equilateral triangle can be a right-angled triangle (it can’t).
• Trying to create a triangle with two right angles—it’s not possible!

Relation to Other Concepts

Understanding the types of triangles helps with area of a triangle, properties of triangles, and is directly connected to types of angles in geometry.

Classroom Tip

A fast way to remember: “EIS” — Equilateral (all sides equal), Isosceles (two sides equal), Scalene (no sides equal). Make a triangle types chart for your notebook or study table. Vedantu’s practice worksheets provide more examples like this for quick learning.

We explored types of triangles—from definitions, key formulas, solved examples, mistakes to avoid, and their importance in other math topics. For more practice and in-depth explanations, visit Vedantu regularly and check out our triangles worksheet collection for instant downloads.