What Is the Pythagoras Theorem and How Does It Work

What Is the Pythagoras Theorem and How Does It Work


Understanding how to measure shapes is a critical feature of geometry.  Connections are fascinating to scientists and mathematicians. They investigate how a plant or animal interacts with its surroundings, as well as the relationship between numbers and nature, and music. They give it a name and share the knowledge when they find a specific relationship repeatedly. The Pythagorean Theorem, which defines the relationship between the sides of a right triangle, is one such example. Pythagoras was a Greek mathematician who contributed significantly to the field of mathematics. He was a superb philosopher and a politician as well. The book Magna Graecia mentions his political ideas. There is a theorem known as Pythagoras Theorem that is quite important in our academic careers. In this blog on education, we will discuss what is the Pythagoras Theorem and how does It work.

The Triangle’s Anatomy

You must first understand a few terms before learning about the Pythagorean Theorem.

(Image: Right Angled Triangle)
  • Right Angled Triangle – A right-angled triangle contains one ninety-degree angle, which is known as a right angle. A box is frequently used by mathematicians to indicate the proper angle. 
  • The Hypotenuse – In a right triangle, the hypotenuse is the side directly across from the right angle. It is the only side of the triangle that is not a part of the right angle. On the diagram, the hypotenuse is green.
  • The Exponents – Exponents are a shorthand means of expressing how many times a number, therefore, referred to as the base number, is multiplied by itself. A number that has an exponent is said to be “raised to the exponent’s power.”

A Pythagorean Theorem is a mathematical theorem that states that

(Image: Pythagorean Theorem)

When c is the hypotenuse and a and b are the sides creating the right angle, the Pythagorean Theorem describes the relationship between the sides of a right triangle. The formula is as follows:

a² + b² = c²

“A-Square + B-Square Is Equal To C-Square,” it says.

The Pythagoras Theorem in the Real World Scenarios

The following are some real-life examples of how to present Pythagoras’ theorem to your High school students:


For two-dimensional navigation, the Pythagorean Theorem is important. You can use it in conjunction with two lengths to calculate the shortest route.  The two legs of the triangle will be north and west, and the shortest line linking them will be diagonal. Aerial navigation can be based on the same concepts.

Drawing on a Facade

Artists use scaffolding to paint on high buildings, and Pythagoras theorem is frequently used to help them finish their work. The painter must assess the height of a ladder required to carefully place the base away from the wall and avoid tipping it over.


Cartographers use surveying to calculate the quantitative distances and heights between different sites before creating a map. Surveyors must create methods for taking systematic measurements since geography is frequently uneven. The Pythagorean Theorem is thus used to calculate the slope of a hill or mountain. A surveyor examines through a telescopic device at a fixed distance away from a measuring stick, forming a right angle between the telescope’s line of sight and the measuring stick. The surveyor may use the theorem to find the length of the slope that covers that distance because he knows both the height of the measuring stick and the horizontal distance of the stick from the telescope.

Construction and Design

The Pythagorean Theorem thus enables you to compute the size of the diagonal connecting two horizontal lines. A program commonly used in architecture, woodworking, and other types of physical creation. So, let’s imagine you’re constructing a sloped roof. If you know the height of the roof and the length it must cover, you can use the Pythagorean Theorem to determine the diagonal length of the roof’s slope. You can use this information to cut suitably sized pillars to support the structure or to determine how much shingling you’ll need.

Demonstrate the theorem for yourself!

  • Obtain a paper pen and scissors, and then follow the instructions given below:
  • On the paper, draw a right-angled triangle with lots of room between the points.
  • Along the hypotenuse, also draw a square (the longest side)
  • On the other side of the hypotenuse, draw a square of the same size.
  • Draw lines like this, as demonstrated below:
  • Cut it in a square shape
  • Make the shapes by cutting them out.
  • Finally, Arrange them in such a way that you can show that the large square has the same area as the two squares on the opposite sides.

To Conclude

The Pythagoras theorem is a fundamental part of mathematics that helps us understand the relationship between the length of certain sides of a right triangle. A crucial theorem that is used in a variety of applications. When applied to real-world examples, it can help us make better decisions and solve problems. By understanding how the theorem works, students can better understand mathematics and physics which will help them in their future education. We hope you have found this information helpful!

Leave a Comment

Your email address will not be published. Required fields are marked *