## Introduction to Right Triangle

When you are studying geometry, there is a chance that you might come across a wide range of figures that vary in shapes and sizes. Each and every single one of the figures has different properties that make them unique. In this section, we are going to discuss a particular figure known as the right triangle. You will get to know the right triangle formula, types and much more from here.

### Right Angle

An angle that is exactly equal to 90 degrees is called a right angle and there are various real-life examples of the right angles in our daily life. For example, the corner angle of a book, edges of the cardboard, etc. Any object with square and rectangular shapes will have its corners equal to 90 degrees or right angle.

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Before you get into the formulas for the area and volume of the right angle triangle, you need to know about the properties that are exhibited in the triangle. The triangle can be defined as a figure that is closed. It is basically a polygon that has about 3 sides in total. There are 3 different vertices of a triangle. With the 3 enclosed sides of the triangle, there is a formation of the 3 interior angles. One of the main things to notice about the right angle triangle is that the sum of all the angles in the interior is always 180 degrees in total. Here we are going to discuss some of the important formulas that you need to know about.

### Right angled Triangle

A triangle that has one of its angles equal to 90 degrees is called a right-angled triangle. The right-angle side of the triangle is perpendicular and the base of the triangle. The third side of the triangle is called the hypotenuse, which is the longest side of all three sides.

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### Formula for Area of Right-Triangle

The formula area of a right triangle,

Area of a triangle = \[\frac{1}{2}\] bh

Where,

b is the base or adjacent side of the right triangle.

h is the height of the right triangle.

### Formula for Perimeter of Right-Triangle

The perimeter of a right triangle is the total length covered by the outer boundary or the sum of all three sides of the triangle.

The formula perimeter of a right triangle,

Perimeter of a right-angled triangle = a + b + c (sum of all the three sides.)

Where a, b, and c are the length of three sides of the right triangle.

### Pythagoras Theorem for a Right Angle Triangle

Pythagoras Theorem is one of the most important theorems in geometry. This is a theorem that is used in order to find the diagonal of the triangle formula. The three sides of the right triangle are interrelated to each other. This relationship between the sides of the triangle is expressed through the Pythagoras theorem.

Hypotenuse² = Perpendicular² + Base²

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According to the theorem, if we are familiar with the two different sides of the right triangle, then it will be very easy to find the right side. The Pythagoras theorem states that.

**1. What is pythagoras theorem in a right-angled triangle?**

The Pythagoras theorem, also known as the Pythagorean theorem, states the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse of the triangle is equal to the sum of the squares of the other perpendicular and base sides of a right-angled triangle. If ABC is a triangle, where AB is the perpendicular side, BC is the base and AC is the hypotenuse of the right-angled triangle.

The Pythagoras theorem is written as AC² = BC² + AB².

**2. What is a right triangle?**

An angle that is exactly equal to 90 degrees is called a right angle. The hypotenuse is the longest side of the right triangle, and the other two sides are the height and the base.

**3. Is it possible to have two right angles?**

No, It is impossible for a triangle to have 2 right angles. We know that a triangle consists of 3 sides and the sum of interior angles of the triangle, sums up to 180°. Consider, if a triangle has two right angles (90 degrees), then the third angle will have to be 0 degrees which means the third side will overlap with another side of the triangle. Hence, a triangle with 2 right angles is not possible.