## Triangle -Geometry Formulas

### Triangle

Triangle is a closed polygon with minimum numbers of sides i.e. three. It is the easiest polygon which works as the base for other polygons with more number of sides. This also represents the smallest stable closed shape. Two very basic rules for a triangle are:

1. The sum total of all three angles will be 180o

If angle A, angle B, and angle C are three angles in a ΔABC, then:

If∠A,∠B,and∠C are three angles in a ΔABC,then:

∠A+ ∠B+∠C=180o

1. The sum of any two smaller sides will be always larger than the biggest side.

If the length of two smaller sides in Δ ABC are a and b and the largest side length is c, then: a+b> c

Where,

A,b,c- Length of three sides

H -Height of the triangle

∠A,∠B,and∠C -Angle measurements of the triangle

P = a + b + c

### Area of a triangle:

A = (b x h)/2

If only two sides and an internal angle is given then the remaining sides and angles can be easily computed by using the formula given below:

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

### Types of Triangles:

Triangles are of different types. Some of these are:

### 1. Equilateral Triangles:

The Equilateral Triangles have the following properties:

• Three sides with equal length
• Three angles all equal to 60o
• Three lines of symmetry

### 2. Isosceles Triangles:

The Isosceles Triangles have the following properties:

• Only two sides of equal length
• Only two equal angles
• One line of symmetry

### 3. Scalene Triangles:

Scalene triangles have the following properties

• All sides of different equal lengths
• All angles are different
• No lines of symmetry

### 4. Acute triangles:

Acute triangles have all acute angles i.e. angles less than 90o

### 5. Right Triangles:

The Right Triangles is having one right angle i.e. equal to 90o

### 6. Obtuse triangles:

Obtuse triangles have one obtuse angle i.e. angle which is greater than 90o