Pythagorean Theorem [Definition, Formula, Equation & Worksheet]

“Mathematics is not about Numbers, Equations, computation or algorithms: it is about understanding”.                                                                                                                        – William Paul Thurston

The mathematics is all about understanding. You don’t need to get feared from the term mathematics and theorem included in it. You just need to keep your mind set that mathematics is all about understanding. If your teacher has assigned you some mathematics work or said that you need to have some information regarding Pythagorean Theorem. And you have mathematics phobia like most of the peoples’ have. There is no need to scare. Mathematics is based on interesting facts. You just need to understand these concepts.  No need to cram mathematics. Understand the theorems. Here, I will explain all about the Pythagorean Theorem in this article. I will discuss what Pythagorean Theorem is, formula if Pythagorean Theorem how to calculate the Pythagorean Theorem with examples. So, let’s begin with this article.

What is the Pythagorean Theorem?

Pythagorean Theorem, also known as Pythagoras theorem, it is related to the Euclidean Geometry. It is basically theorem which states that in the right angle triangle the square of two sides is equal to the square of third side. Or we can say the square longest side is same as the sum of the square of remaining two sides. Pythagoras theorem is used to find out the length of the missing side of triangle. It helps a lot in real life also in the construction work when have to built buildings or make an angle of elevation or depression. So, you can also learn this theorem with the help of real life examples, which you can easily imagine.

Pythagorean Theorem Definition

If a right angled triangle has sides “a”, “b”, and “c” and suppose c has the longest side, then the summation of squares a and b will be same as the square of c. This is the simple definition you can write or define when you have to definition of Pythagorean Theorem. This longest side is known as the “Hypotenuse” and vertical line is known as which makes 90 degree angle with other side is known as “perpendicular” and rest base line or horizontal line is known as “base”. These are mathematical expressions you need to remember them if you want to understand the theorem.

Define Pythagorean Theorem

Pythagorean Theorem or Pythagoras theorem is based on very simple calculation of sides of right angled triangle. It helps a lot in solving algebra problems in mathematics. Pythagorean Theorem is considered as very important as compare to others in academic studies. If you are a mathematics lover and you want to sharp your skills in algebra portion try to learn Pythagorean Theorem.

Pythagorean Theorem Calculator

If you are unable to learn Pythagorean Theorem and you have to solve the unsolved sums based on this theorem then need not to worry in this era of technology. There are many Pythagorean Theorem calculators available online, you just need to enter values of the sides and it will give you the accurate answer. And if you got success in solving Pythagorean Theorem sums but you want to recheck your calculation, you can take help of this calculator to confirm your solution.

Pythagorean Theorem Formula

Pythagorean Theorem formula is very easy to remember as I have discussed above as well. And it is mathematical represented as

a2 + b2 = c2

Here, a, b, and c are the sides of the right angle triangle. Where “a” is the perpendicular and b is base. C is longest side or you can say hypogenous of the right angled triangle.

Pythagorean Theorem Calculation: Find a, b = n/a, c = n/a

Here, is a particular situation I am stating so, that you can easily get the concept of how to solve sums based on Pythagorean Theorem. In the above-mentioned statement you need to find out the side a where other two sides are given to you. And you can notice one thing tht both the sides of this statement are same. In this scenario, you just need to remember that the third side will be square root of 2 with same value of side. I.e. a will be equal to the √2(n/a). or we can also write square of a will be equal to the twice of the square of n/a.

a2 = 2(n/a)2

Pythagorean Theorem worksheet

There are many Pythagorean Theorem worksheets available on the internet with the help of which you can take help of these worksheets to build your skills in Algebra. And can solve complicated calculations of this theorem very easily without the help of calculator. These small things play a vital role in sharpening your skills and build your confidence in mathematics. These worksheet are easily available online you can do daily practice on these and then after some time you will find this theorem as the most simple theorem of the mathematics.

Pythagorean Theorem Proof

You want to know about the proof of this theorem then here I will also provide you the proof of Pythagorean Theorem as well. The proof of Pythagoras Theorem is very simple you just need to build a right angle triangle and then make square on the each side of this triangle. When you are done with drawing this triangle, then find out area of these squares. When you are done with finding area of each square individually then you will find out that the longest side area of square is equal to the sum of other two sides area of square. This is the Pythagoras Theorem. Yes, t is all we need to proof Pythagoras Theorem. And it is really very simple. You can proof this simply by drawing right angle triangle with the help scale and will easy to proof with the help values. Then you can covert these values to the random option like x, y, z or a, b, c.


Pythagorean Theorem Examples

To learn or understand Pythagorean Theorem, you can take help of examples like take sides of the right angle triangle 3 cm and 4 cm and try to find out length of longest side. Here the length of the longest side will be equal to the sum of square of 3 and 4. I.e.  “a” and b are 9 and 16 respectively. And the sum of 9 and 16 is 25. And 25 is the square root of 5. That means the length of the longest side is 5 cm.

C2 = 32 + 42

C2 = 9 + 16

C2 = 25

C = 5     ;


Pythagorean Theorem word problems

There are many problems you will get in the word format. To understand the concept of Pythagorean Theorem, you can take help of these problems and try to solve these for better understanding of the theorem. The questions will be statement based and these questions will also help you to relate this theorem with real world as well. The word problem can be in the form that a person walks 3 cm west then turns right side and moves 4 cm how much total distance will be covered by the person. While solving such kind of word problems you will get to understand this theorem and calculations gradually.

Pythagorean Theorem Equation

The Pythagorean theorem equation is very simple it just takes three sides as a, b, and c. and you just only need to write these sides in the mathematical form as square of a equals to sum of square of b and c.

i.e.              Equation of Pythagorean Theorem:     a2 = b2 + c2    


Converse of Pythagorean Theorem

There is converse statement of this Pythagorean Theorem as well. As in the Pythagorean Theorem we state that in the right angle triangle, the sum of squares of two sides is equal to the square of the third longest side.

Similarly in the converse with the help of theorem we need to proof the triangle is right angle triangle. i.e. if the sum of square of two sides is equal to the square of third side then the triangle will be considered as right angle triangle.

Pythagorean Theorem Identities

The trigonometric expressions are considered as identities of the Pythagorean Theorem. i.e. the angle between Hypogynous and base is considered as theta. Here, I am sharing the sample image of these identities of this theorem, which elaborates the huge concept of trigonometry in the mathematics. But here these identities are used with some basic proved rules.

Pythagorean Theorem calculator with Angles

In case of angles you need to calculate the identities of the right angle triangle and with the help of these identities you will be able to calculate the length of the sides of the right angle triangle. There is online calculator available for the calculation of the sides with the help of angles. You just need to enter the values of the angles in this calculator and you will get the desired result from this.

Pythagorean Theorem worksheets PDF

There is also option of a worksheet in the PDF folder also. You can save the worksheet in the PDF forms and then can solve the theorem questions for improving your skills in this. There are many PDF format worksheets available on the internet as well. You just need to download these worksheets and can perform your task and solve these questions. These worksheets help a lot in practicing sums and for the better understanding of the theorem.

So, it is all about Pythagorean Theorem I discussed with you in this article. I hope this article will help you in a better understanding of the theorem and you will try to solve sums based on this theorem and definitely get accurate answers by doing practice. Pythagoras Theorem is considered as very simple as basic theorem which helps to solve real life problems as well. So, it is also considered as very important theorem also from the academic point of view as well as competitive or architecture purposes as well. Hope you get all the answer and tips from this article for the betterment of your mathematics skills.