A triangle is a three-dimensional plane figure with three angles. In a triangle, the three interior angles always add up to 180°.

### Properties of a Triangle:

**a.** A triangle has three sides, three angles, and three vertices.

**b.** A sum of the angles in a triangle = **180°**

**∠**A + **∠**B + **∠**C = 180°

**c.** The **height **“**h**” of a triangle is the length of a line segment that connects the **base** “**b**” to the opposite vertex and makes a 90° angle with the base.

The base of a triangle refers to any side of a triangle, which is perpendicular (makes a 90° angle) to its height or altitude.

**d. **Any side of a triangle is less than the sum of two other sides and greater than their difference.

**e.** The side opposite to the largest angle of a triangle is the largest side.

### Types of Triangles:

Triangles can be broadly classified into two types, which are:

- Triangles based on the lengths of their sides
- Triangles based on their interior angles

In this topic, we will be discussing these two classifications of triangles along with their properties.

### Classification of Triangles:

S/n | Based on their Sides | Based on their Angles |
---|---|---|

1. | Scalene Triangle | Acute Triangle |

2. | Isosceles Triangle | Obtuse Triangle |

3. | Equilateral Triangle | Right Triangle |

### Types of Triangles Based on Sides:

### i. Scalene Triangle:

**A scalene** triangle has no equal sides and no angles equal.

### ii. Isosceles Triangle:

**An isosceles **triangle has two adjacent sides equal and two angles equal.

### iii. Equilateral Triangle:

An** equilateral **triangle has all its sides equal and all its angles equal. Each angle is 60°.

### Types of Triangles Based on Angles:

### i. Acute Triangle:

An **acute-angled **triangle has each of its angles less than 90° i.e. each angle is acute.

**Note:** A scalene may not always be an acute triangle. It can be a right-angled triangle with angles of 90°, 40°, and 50°. A scalene triangle can also be an obtuse triangle with angles 20°, 50°, and 110°. Three interior angles of an acute triangle **must** be less than 90°.

### ii. Obtuse Triangle:

An **obtuse-angled** triangle has one of its angles greater than 90°.

### iii. Right-angled Triangle:

- A
**right-angled**triangle has one of its angles equal to 90°.

- The opposite of the right angle is the longest side and it’s often called the
**hypotenuse**.

Also, note that a right-angled triangle **must** have two acute angles. As a right triangle has one angle equal to 90°, this means the sum of the remaining two angles must be 180° – 90° = 90°. So the remaining two angles must be acute and can be 60° + 30°, or 55° + 35°, etc.

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