**What is Pythagoras Theorem**

According to Pythagoras theorem “**In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.**“ It is applicable only for the right-angled triangle.Pythagoras Theorem Proof & its application is explained here.

Each side of a right triangle has a name:

Where

“a” is the perpendicular or Opposite side,

“b” is the base or Adjacent,

“h” is the hypotenuse side which is the longest side.

According to the definition,

Hypotenuse^{2} = Perpendicular^{2} + Base^{2}

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

**Application of Pythagoras Theorem**

- To find triangle is a right-angled triangle or not.
- In a right-angled triangle, we can calculate the length of any side if the other two sides are given.
- To find the diagonal of a square.

**Pythagorean Theorem Problems**

**Examplem1:** The sides of a triangle are 4,3 & 5 units. Check if it has a right angle or not.

**Solution:** According to Pythagoras Theorem,

Perpendicular2 + Base2 = Hypotenuse2

Perpendicular = 5 units

Base = 3 units

Hypotenuse = 4 units

4^{2} + 3^{2} = 5^{2}

⇒ 16 + 9 = 25

⇒ 25 = 25

L.H.S. = R.H.S.

Therefore, **It is right angle.**

**Examplem2:** The two sides of a right-angled as shown in the figure. Find the third side.

**Solution:** Given;

Perpendicular = p units

Base = 12 units

Hypotenuse = 15 units

As per the Pythagorean Theorem, we have;

Perpendicular^{2} + Base^{2} = Hypotenuse^{2}

⇒p^{2} + 12^{2} = 15^{2}

⇒p^{2} + 144 = 225

⇒p^{2} = 225 – 144

⇒p^{2} = 81

⇒p = √81

Therefore,** p = 9 units**

I hope, this article will help you lot to understand the Pythagoras Theorem Proof, its application, & in solving various problems related to this article, if you still have any doubts related to this article, you can ask it into the comment section. If you have any problem in any topic mathematics you can post your problem in the comment section. You will get a reply shortly.