Pythagoras theorem gives us relation between among the three sides of right angle triangle. It has three angles so we called its triangle whose right angle that is 90 degrees with respect to other side. There are three side of triangle first one hypotenuse other two side base and perpendicular .If we related this term in mathematics form or Pythagorean so it’s would be like c^{2}=a^{2}+b^{2}

It is known by two names one is Pythagoras theorem and Pythagorean. Its say about square of length of hypotenuse is sum of the two side of square of length of right angle triangle.

As you can see in image that there is three side of triangle where opposite to 90 degree always will be hypotenuse and adjacent side is known as base and reaming side is perpendicular.

**Pythagoras theorem basic concept **

there are three side of triangle as you can see upper image where a=base side, b=perpendicular site, c=hypotenuse side as we also can write this equation like **Hypotenuse ^{2} = Perpendicular^{2} + Base^{2}**

## Application of Pythagoras theorem

- Construction and architecture

- Its used for justify that building is square or not.

- Its is used in navigation

- It used in survey

## based on Pythagoras theorem example

Here is fist question:

**calculate the hypotenuse of triangle whose one side is 2 cm and second side is 5cm.**

**Answer:** using Pythagoras theorem formula we are going to find answer.

Here we known two side of triangle length

One side is given =2 cm

Another side is given =5cm

So here we going to apply direct formula which is c^{2}=a^{2}+b^{2}

C^{2}=2^{2}+4^{2}

C^{2}=4+4

C^{2}=8

C=2.8(final answer )

**Find out one side length if given value is c=8 and b=4**

**Answer:** using Pythagoras theorem formula we are going to find answer.

c^{2}=a^{2}+b^{2}

8^{2}=a^{2}+4^{2}

a^{2}=8^{2}-4^{2}

a^{2}=64-16

a^{2}=64-16

a^{2}=48

a=4.6(final answer )

## Pythagoras Theorem Proof

So if we are looking to proof this theorem here we have to draw right angle triangle as per give image which is ABC in which draw perpendicular line BD whose meeting with AC at D.

Here is Proof of theorem

We know, △ADB ~ △ABC

AD/AB=AB/AC

AB^{2 }= AD × AC (sides of similar triangles)

Also, △BDC ~△ABC

CD/BC=BC/AC (sides of similar triangles)

BC^{2}= CD × AC (2)

Adding the equations (1) and (2) we get,

AB^{2 }+ BC^{2 }= AD × AC + CD × AC

AB^{2 }+ BC^{2 }= AC (AD + CD)

Since, AD + CD = AC

Therefore, AC^{2} = AB^{2} + BC^{2}

So the Pythagorean theorem is proved.

## Frequently Asked Questions – FAQs

### What is the formula for Pythagorean Theorem?

here is formula for Pythagorean c^{2}=a^{2}+b^{2}or Hypotenuse^{2} = Perpendicular^{2} + Base^{2}

### What is the formula for hypotenuse?

we can write Pythagorean Theorem is another ways which is **c = √(a ^{2} + b^{2})**

### Should we apply the Pythagoras Theorem for any triangle?

no you cant apply this formula of all triangles its only applicable for right-angled triangle.

### Application of Pythagoras theorem

Pythagoras theorem is mostly used where we want check distance between two points.