# Types of Triangles – Definition With Examples

## What is a Triangle?

A triangle is a polygon made up of three sides. The point where two sides of the triangle meet are called the vertex and form an interior angle. All triangles have three sides, three vertices, and three interior angles.

Consider a triangle with three vertices as A, B and C are denoted as △ABC, as shown below.

## Basic Properties of Triangles

• A triangle has three interior angles, and the sum of all the interior angles in a triangle is 180°. This is known as the angle-sum property of a triangle.
• A triangle has three sides. The total length of any two sides of a triangle is greater than the measure of the third side. This is also known as the triangle inequality property.
• The longest side of the triangle is opposite its biggest angle, and the side opposite the smallest angle is the shortest side of the triangle.

## What are the Different Types of Triangles?

A triangle is a closed 2-dimensional shape with three sides. There are different names for the types of triangles. Based on the length of the sides, there are three types of triangles: scalene, isosceles and equilateral triangles. A triangle’s name also depends on the measure of its interior angle: acute (if all angles are less than 90°), right (if one angle is 90°), and  obtuse (if one angle is more than 90°)

The figure given below shows the various types of triangles and their properties.

## Classification of Triangles Based on Side Lengths

There are three types of triangles based on the measure of their sides.

### Scalene Triangles

All sides of a scalene triangle are of different lengths. Consequently, the three interior angles are different from each other.

### Isosceles Triangles

An isosceles triangle has two sides of equal length. The angles opposite to these equal sides are equal.

### Equilateral Triangles

The three sides of an equilateral triangle are of equal length. Consequently, each interior angle of equilateral triangles is equal to 60°.

## Classification of Triangles Based on Interior Angles

In geometry, there are various types of angles based on measurement. The interior angles of a triangle can be of three kinds: namely acute, right, or obtuse angles, as shown below.

There are three types of triangles based on the measure of interior angles.

### Acute Triangles

All interior angles in an acute triangle are acute angles, i.e., they measure less than 90°.

### Right Triangles

The triangle with one interior angle of 90° or a right angle is called a right triangle. Hypotenuse, the side opposite the right angle, is the longest side in a right triangle.

### Obtuse Triangles

The triangle with one interior angle greater than 90° or an obtuse angle is called an obtuse triangle.

## Solved Examples

Example 1: Classify the triangle as equilateral, isosceles, or scalene.

Solution:

Examine the lengths of the sides to see if any sides are equal. All sides of the triangle are different from each other.

Therefore, the triangle is scalene.

Example 2: Classify the triangle as acute, right, and obtuse.

Solution:

Examine the measure of each interior angle of the given triangle and compare it to 90°. All the angles of the triangle are less than 90°.

Therefore, the triangle is acute.

3. In an isosceles triangle, ABC, ∠A = 100° and ∠B  = ∠C. Find the measure of  ∠C.

Solution:

Following the angle sum property of a triangle, we get

∠A + ∠B  + ∠C = 180°

So, ∠B  + ∠C = 180° – 100° = 80°

Since ∠B  = ∠C, measure of ∠C = 80° ÷ 2 = 40°

## Practice Problems

1

### What type of triangle is in the image given below? Right triangle
Obtuse triangle
Equilateral triangle
Isosceles triangle
CorrectIncorrect
Two sides of the triangle are equal. Therefore, it is an isosceles triangle.
2

### If the two angles of a triangle are 45° and 60°, what is the third angle? Classify the triangle.

105°; obtuse
57°; scalene
75°; acute
75°; obtuse
CorrectIncorrect
According to the angle sum property, the third angle must be 180° - 45° - 60° or 75°. All the
interior angles are less than 90°. Therefore, the triangle is acute.
3

### Which of the following cannot be the sides of a scalene triangle?

7 ft, 13 ft, 14 ft
6 cm, 8 cm, 10 cm
24 m, 10 m, 26 m
15 cm, 15 cm, 15√2 cm
CorrectIncorrect
Correct answer is: 15 cm, 15 cm, 15√2 cm
All sides of a scalene triangle must have different lengths.
4

### In a right triangle, if angle A measures 30°, find B. 30
60°
90°
150°
CorrectIncorrect
According to the angle sum property, ∠B = 180° -∠C -∠A = 180° - 90° - 30° = 60°

## Conclusion

In this article, we learned about the types of triangles. They can be classified based on their sides and angles. To learn more math topics in a fun and interactive way, visit SplashLearn, the game-based learning platform.