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What is Pythagoras' Theorem?-formula, History, Equation | Gurugrah.in





What is Pythagoras' Theorem? –

Pythagoras theorem –

The Pythagorean Theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle. We can learn more about the Pythagorean theorem, its derivatives, and equations by studying examples of theorems applicable to triangles and squares.


What is Pythagoras' Theorem? –

The Pythagorean Theorem states that if a triangle is at right angles (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Look at the following triangle ABC where we get BC 2 = AB 2 + AC 2. The base, AC, is the length of the hypotenuse, BC. The height, AB, is the length of the other side AD of the triangle. It is important to note that the hypotenuse is the longest side of a right triangle.


Pythagoras theorem formula –

The Pythagorean Theorem formula states that in a right-angled triangle ABC, the square of the hypotenuse is equal to the sum of the squares of the other two legs. If AB and AC are sides and BC is the hypotenuse of the triangle, then: BC 2 = AB 2 + AC 2. In this case, AB is the base, AC is the height, and BC is the hypotenuse.


Pythagoras Theorem Equation –

The Pythagorean theorem equation can be expressed as C2 = A2 + B2 where C is the vertices of the equator triangle and A and B are the other two legs. Therefore, any triangle with an angle equal to 90 degrees can be solved by using the Pythagorean theorem equation.


History of Pythagoras Theorem –

The Pythagorean Theorem Theorem was discovered by the Greek mathematician Pythagoras theorem. He was an ancient Greek philosopher from Ionia. He created a group of mathematicians who worked passionately on numbers.


PROOF of Pythagoras Theorem –

In a right-angled triangle, the base and the perpendicular make an angle of 90 degrees with each other. Therefore, according to Pythagoras’ theorem, “the square of the hypotenuse is equal to the sum of the square of the base and the square of the perpendicular.

“the square of the hypotenuse is equal to the sum of a base square and perpendicular square.”


To prove this theorem, suppose that there is a triangle ABC whose angle B is right-angled.


We have to prove: AC²= AB² + BC²


To explain: We draw a straight line BD which meets AC at D.


Proof:

We know by the theorem that if a right-angled triangle is drawn from the hypotenuse of a right-angled side, then two triangles on both sides of the perpendicular are similar to each other.


So,

△ADB ~ △ABC

Hence,

AD/AB = AB/AC (Condition for similarity)

Or,

AB2 = AD × AC (1)

Also, △BDC ~△ABC (By applying the same theorem)

Therefore, CD/BC = BC/AC (Condition for similarity)

Or, BC2= CD × AC (2)

Now,

By adding the equations (1) and (2) we get,

AB2 + BC2 = AD × AC + CD × AC

AB2 + BC2 = AC (AD + CD)

Since, AD + CD = AC


Therefore, AC2 = AB2 + BC2


Applications of Pythagoras Theorem –

• To determine whether a triangle is right angled.

• Find the diagonal of the square.

• In a right-angled triangle, if we know the lengths of the other two sides, we can calculate the length of either side.


IMPORTANT QUESTION ANSWER | FAQ –


1. What is called the Baudhayan theorem?

Answer:- Pythagoras' theorem is called the Baudhayan theorem.


2. What is the formula of the hypotenuse?

Answer:- Hypotenuse is the longest side of a right triangle, which is opposite to the right angle, which is adjacent to the base, and perpendicular C = (a2 + b2), where c is the hypotenuse and a and b are the base and perpendicular.


3. What is the formula of the Pythagoras theorem?

Answer:- Formula of Pythagoras theorem: (hypothesis)2 = (perpendicular)2 + (base)2 That is, (AB)2 + (BC)2 = (AC)2



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By Chanchal Sailani | September 27, 2022, | Editor at Gurugrah_Blogs.

 

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