**What is a triangle?**

**As the name suggests, the triangle is a polygon that has three angles. So, when does a closed figure has three angles?**

**A close figure having three side.**

Thus, we can say that a triangle is a polygon, which has three sides, three angles, three vertices and the sum of all three angles of any triangle equals 180°.

**Properties of a triangle**

**These are the properties of a triangle:**

- A triangle has three sides, three angles, and three vertices.
- The sum of all internal angles of a triangle is always equal to 180
^{°. }This is called the angle sum property of a triangle. - The sum of the length of any two sides of a triangle is greater than the length of the third side.
- The side opposite to the largest angle of a triangle is the largest side.
- Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

**Types of triangles**

**Triangles can be classified in 2 major ways:**

**Classification according to internal angles – 3****Classification according to the length of its sides – 3**

### Classification of a triangle by internal angles

**Based on the angle measurement, there are three types of triangles:**

**Acute Angled Triangle****Right-Angled Triangle****Obtuse Angled Triangle**

**Let us discuss each type in detail.**

**Acute Angle Triangle**

**A triangle that has all three angles less than 90° is an acute angle triangle.**

- So, all the angles of an acute angle triangle are called acute angles

**Right-Angle Triangle**

**A triangle that has one angle that measures exactly 90° is a right-angle triangle.**

- The other two angles of a right-angle triangle are acute angles.
- The side opposite to the right angle is the largest side of the triangle and is called the hypotenuse.

**In a right-angled triangle, the sum of squares of the perpendicular sides is equal** to the square of the hypotenuse.

For e.g. considering the above right-angled triangle ACB, we can say:

**(AC) ^{2} + (CB)^{2} = (AB)^{2}**

This is known as __Pythagoras theorem__

Vice versa, we can say that if a triangle satisfies the Pythagoras condition, then it is a right-angled triangle.

**Obtuse/Oblique Angle Triangle**

**A triangle that has one angle that measures more than 90° is an obtuse angle triangle.**

Given below is an example of an obtuse/oblique angle triangle.

**Classification of triangles by length of sides**

**Based on the length of the sides, triangles are classified into three types:**

**Scalene Triangle****Isosceles Triangle****Equilateral Triangle**

**Let us discuss each type in detail.**

**Scalene triangle**

**A triangle that has**is a scalene triangle.__all three sides of different lengths__**Since all the three sides are of different lengths, the**__three angles will also be different.__

**Isosceles triangle**

**A triangle that has**is an isosceles triangle.__two sides of the same length and the third side of a different length__**The**__angles opposite the equal sides measure the same.__

**Equilateral triangle**

**A triangle which has**is an equilateral triangle.__all the three sides of the same length__**Since all the three sides are of the same length, all**__the three angles will also be equal.__**Each interior angle of an equilateral triangle = 60°**

**Special cases of Right Angle Triangles**

Let’s also see a few special cases of a right-angled triangle

**45-45-90 triangle**

**In this triangle,**

- Two angles measure 45°, and the third angle is a right angle.
- The sides of this triangle will be in the ratio – 1: 1: √2 respectively.
- This is also called an
since two angles are equal.__isosceles right-angled triangle__

**30-60-90 triangle**

**In this triangle,**

- This is a right-angled triangle, since one angle = 90°
- The angles of this triangle are in the ratio – 1: 2: 3, and
- The sides
*opposite to these angles*will be in the ratio – 1: √3: 2 respectively - This is a
since all three angles are different.__scalene right-angled triangle__

**The formula for Area of Triangle**

- Area of any triangle = ½ * base * height
- Area of a right-angled triangle = ½ * product of the two perpendicular sides