What is the theorem of Pythagoras.

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Pythagoras is an ancient Greek philosopher and mathematician. He worked on geometric proofs and showed that triangles, with lengths in the ratio 3:4:5, always exist in a triangle with a right angle. Having listened to musical harmonies and how different notes were obtained, he was able to determine a connection between numbers and musical intervals.  

Pythagoras's theorem relates the length of the hypotenuse of a right-triangle to the lengths of the other two sides. The hypotenuse is always the longest side. The theorem can be written using algebra where the letters `a` and `b` are often usedd to represent the first two sides and `c` the hypotenuse (always opposite the right angle). It is also popular to use `x` and `y` such as they exist on the Cartesian plane as the x-axis and y-axis with` r` (or `h` ) representing the hypotenuse. The theorem is also used for the equation of a circle with the origin `(0;0)` as the center.

Ans: The square on the hypotenuse equals the sum of the squares of the other two sides and can be written as:  

`a^2 + b^2 = c^2`  or `x^2 +y^2 = r^2`

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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Pythagoras' theorem is known as the Pythagorean Theorem.

In a right triangle, them sum of the squares of the two legs is equal to the square of the hypotenuse.

a = leg

b = leg

c = hypotenuse

`a^2+b^2=c^2`

For instance if given two legs of a right triangle, 2 cm and 4 cm, you can find the length of the hypotenuse.

`2^2+4^2=c^2`

`4+16 = 20 = c^2`

`c=sqrt(20)`

This is the length of the hypotenuse.

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malkaam | Student, Undergraduate | (Level 1) Valedictorian

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The Pythagoras or the the Pythagorean Theorem is named after a greek mathematician Pythagoras. It can be defined as a right angled triangle with 2 sides supporting the third called hypotenuse. Given below is the derivation of the Pythagoras Theorem:

Area of trapezoid = Area of 3 triangles

1/2(a+b)(a+b)=1/2ab+1/2c^2+1/2ab` `

(a+b)^2=ab+c^2+ab

a^2+2ab+b^2=2ab+c^2

a^2+b^2=c^2

Proved by U.S. Pres. James Garfield` `    

Where a=1 side, b=1 side and c=hypotenuse

The above formula is used to find the hypotenuse.

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kevin0001 | Student, Grade 9 | (Level 1) Salutatorian

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The theorem of Pythagoras was theorem used only for right triangles. The creator of the system , Pythagoras, was a Greek mathematician  who was named after it. It is commonly known as the Pythagorean Theorem. It is used in geometry and states that the square of the hypotenuse of a right triangle is equal to the sum of the remaining sides squared. the equation used for it is : `a^2 + b^2 = c^2`

with a and b being the two sides and c being the hypotenuse.

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melissa1106 | Student, Grade 11 | (Level 1) Salutatorian

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The Pythagorean theorem is used to find a missing side of a right triangle. the formula is known as:

A represents one of the legs, B represents another leg and C is the hypotenuse of the right triangle. Side C should always be the longest and it should be directly across from the 90 degree angle.

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mmenon | Student, Grade 12 | (Level 3) eNoter

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Pythagoras's theorem - commonly known as The Pythagorean Theorem- is used to find a side of a right triangle given the value of the other two sides. The formula `A^2 +B^2 =C^2` is used given that C is the side opposite the right angle(the hypotenuse), while A and B are the other two sides. 

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mchandrea | Student, College Junior | (Level 1) Salutatorian

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The Pythagoras theorem or better known as the Pythagorean theorem falls under Right Triangle Trigonometry. It states that 

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two remaining sides.

In equation form: 

a and b are the two sides; which may not necessarily have the same lengths and c is the hypotenuse. The hypotenuse is the longest side of the triangle.

Take note that the Pythagorean theorem can only be applied to right triangle.

This formula is used when one of the missing sides are to be calculated.

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mchandrea | Student, College Junior | (Level 1) Salutatorian

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The equation for my answer above should be this: `A^2 + B^2 = C^2`

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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Pythagorean Theorem is a theorem used to figure out the missing side of a right triangle. The formula is written as:

`a^2 + b^2 =c^2`

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ayl0124 | Student, Grade 12 | (Level 1) Valedictorian

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When dealing with right triangles (triangles that have one 90 degrees angle), the Pythagorean Theorem can be applied. 

`a^2 + b^2 = c^2`

"a" and "b" are the legs of the triangle and "c" is the hypothenuse. The hypothenuse is the longest side of the triangle and is opposite of the legs. 

By knowing two sides of a right triangle, you can easily find the unknown side length. This equation also comes in handy when you are using sine, cosine, and tangent (SOHCAHTOA). 

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chrisyhsun | Student, College Freshman | (Level 1) Salutatorian

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The Pythagorean Theorem is applicable to right triangles, which are triangles in which one of the angles is a 90 degree angle. The theorem, as stated by previous answers, is:

a^2 + b^2 = c^2

The a, b, and c in the equation stand for the three side lengths of the triangle. Side c will always be the longest side and the one across from the 90 degree angle. This is called the hypotenuse whereas the other two (a and b) are referred to as legs. Therefore, the theorem states that the square of the length of leg 1 added to the square of the length of leg 2 is equal to the square of the length of the hypotenuse. This theorem is used when calculating for the missing length of a side of a right triangle.

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ik9744 | Student, Grade 9 | (Level 1) Valedictorian

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The Pythagorean Theorem is :

A squared + B squared = C squared.

Squared = Power of Two [X · X]

A : One side that is not the hypotenuse [A and B can be either side]

B : One side that is not the hypotenuse [A and B can be either side]

C : The last side is the hypotenuse [The side that is longer]

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nisarg | Student, Grade 11 | (Level 1) Valedictorian

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The pythagorean theorem is: 

a is one side

b is the other side

and c is the hypotenuse

this only works with right triangles

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zumba96 | Student, Grade 11 | (Level 3) Valedictorian

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Pythagoras is a well known Greek philosopher and mathematician and was the source of the known Pythagorean theorem we all use. This theorem is often used in math when someone needs to find the hypotenuse of a triangle but can also be rearranged for the sides of the triangles as well. This theorem is a squared plus b squared equals c squared where c is the hypotenuse, and a and b are the legs 

` ```

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jess1999 | Student, Grade 9 | (Level 1) Valedictorian

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The Pythagorean theorem is

The Pythagorean theorem is used to find the side lengths of a right triangle .

A / B = the first two sides of the right triangle

C = the hypotenuse of the right triangle or also known as the longest side of the right triangle

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jess1999 | Student, Grade 9 | (Level 1) Valedictorian

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I forgot to put the actual theorem

but it is

a² + b² = c²

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rachellopez | Student, Grade 12 | (Level 1) Valedictorian

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The Pythagoras' theorem was discovered 2000 years ago and is helpful for solving problems involving right triangles. The formal definition states "the square of the hypotenuse is equal to the sum of the squares of the other two sides." This definition can be summed up with the well known formula ` ` `a^(2)+b^(2)=c^(2)`

A and B represent the two legs of the right triangle and C represents the hypotenuse, or the longest of the three sides. This therom is also known as the Pythagorean Theorem.

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acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

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The pythagorean theorem is: 

`A^2+ B^2 = C^2`

this is the basic method usually used to find out a missing side of a triangle. A and B represent the two sides while c stands for the hypotenuse. 

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archanasah | Student, Undergraduate | (Level 1) eNoter

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without going in terminology way...basically u need to know is this ....Pythagoras theorem is used in right angle triangle only..in which  sum of square of base and square of perpendicular is always equal to the square of hypotenuse. Suppose base of the triangle is "a" & perpendicular is "b"& hypotenuse is "c". Then (a)^2+(b)^2=(C)^2.

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Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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Pythagoras was an ancient Greek mathematician. This theorem is called the Pythagorean theorem. The Pythagorean theorem describes the relationship between the three sides of a right triangle. The slanted side of the triangle, called the hypotenuse is  generally called " c " . The other two sides are called " a "  and " b " . He found the relationship to be: a^2 + b^2 = c^2

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parama9000 | Student, Grade 11 | (Level 1) Valedictorian

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a^2+b^2=c^2

It is interesting to note that this theorem was not actually first discovered by Pythagoras...

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eli468 | Student, Undergraduate | (Level 1) Valedictorian

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Commonly referred to as the Pythagorean theorem, the equation for it is a^2+b^2=c^2. (Read as A squared plus B squared equals C squared.) This theorem applies to triangles. C would represent the hypotenuse or the longest side of the triangle. A and B would be the other two sides. This theorem only works on right triangles i.e. triangles with an angle of 90 degrees.` <br> `

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