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It states that for any right angle triangle that its hypotenuse when squared is equal to the sum of its squared sides.
Since the 4th century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right triangle the square of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the squares of the other two sides.
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In other words, given a right-triangle with side lengths a and b, and a hypotenuse of length c, then
a2 + b2 = c2
Example:
Given a right-triangle with side a = 3 and side b = 4, what is the hypotenuse (side c)?
Solution: a2 + b2 = c2
32 + 42 = c2
(3 x 3) + (4 x 4) = c2
9 + 16 = c2
25 = c2
c = √25
c = 5.
(Note that c can't equal -5 because c is the length of the hypotenuse of the triangle and length must be positive.)
The importance of the theorem goes way beyond triangles, in fact the Pythagorean theorem is the basis for the definition of distance between two points in space of any dimension of size 2 or more.
(There is a related link to 81 different proofs of this theorem.)
Euler Improvement
The mathematician George Euler improved the Pythagoras theorem to apply to all triangles using the cosine of the included angle:
a2 + b2 -2abcosT= c2
where T is the angle between a and b and cos the goniometric function.
(The cosine of 90° is 0 which makes this the Pythagoras theorem.)
Example
IF BC=A=5CM=base of right angle, and AB=B=6CM the perpendicular and AC=C=the hypotenuse.
(HYP)2=(BASE)2+(PERP)2
C2=A2+B2
So we have:
C2=25+36
C2=61
Now we use the square root property but take the positive square root.
So C is approximately equal to 7.81 CM
Generalizing the theorem to higher dimensions
The Pythagorean Theorem works in higher dimensions too. If you have three legs, each one in a different dimension, and each at right angles to the other two, the hypotenuse joining these three lines has a length which equals sqrt(a2+b2+c2). You can't have four mutually right legs in three dimensions, but you can in four dimensions, in which case h=sqrt(a2+b2+c2+d2) and so on.
a squared + b squared = c squared. You square a and square b, and them together and find the square root of that number. that = c
A2 + B2 = C2
it helps find the missing leg also knowen as the Hyptones for any trignal that has congurent sides
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Converse of Pythagorean Theorem?
The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.
What is the difference between the pythagorean theorem and the converse of the pythagorean theorem?
The Pythagorean Theorem states that in a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. The converse of the Pythagorean theorem states that, if in a triangle with sides a, b, c, a2 + b2 = c2 then the triangle is right and the angle opposite side c is a right angle.
Is The Distance Formula is derived from the Pythagorean Theorem?
No.
How do you find the perimeter of a parallelogram using Pythagorean theorem?
you can't, because the Pythagorean theorem is for right triangles and the triangles formed by the diagonal of a parallelogram are not right triangles.
Do biological scientists use the Pythagorean theorem?
Yes.
Was the Pythagorean Theorem proven?
Oh yes, the Pythagorean Theorem has been proven.
What shape does the Pythagorean theorem use?
The Pythagorean theorem uses the right triangle.
What are the aspects of Pythagoras theorem?
There are 19 various aspects of Pythagoras theorem. Pythagorean Theorem (1) Pythagoras Theorem(2) Pythagorean Theorem (3) Pythagorean Theorem (4) Pythagoras Theorem(5) Pythagorean Theorem(6) Pythagrean Theorem(7) Pythagoras Theorem(8) Pythagorean Theorem (9) Hyppocrates' lunar Minimum Distance Shortest Distance Quadrangular Pyramid (1) Quadrangular Pyramid (2) Origami Two Poles Pythagoras Tree(1) Pythagoras Tree(2) Theorem by Pappus
How do you use a Pythagorean theorem with cube?
You can use pythagorean theorem twice to find the diagonal of a cube
What is the standard form of the pythagorean theorem?
the standard form of the Pythagorean Theorem is :a2 + b2 = c2
What are the types of Pythagorean theorem?
The Pythagorean theorem is a2 + b2 = c2
Which character describes the Pythagorean Theorem in 'The Wizard of Oz'?
When the Scarecrow gets his brains, he recites the Pythagorean Theorem.
What cultures used Pythagorean theorem?
The Greek, Babylonian, Indian, and Chines knew and used the Pythagorean Theorem.
Who formulated pythagorean theorem?
The Pythagorean theorem gets its name from the ancient Greek mathematician Pythagoras. He was one of the first to offer proof of the theorem.
What rhymes with the Pythagorean theorem?
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Who named the pythagorean theorem?
pythagorean theorem was named from a greek mathemition called pythagorus (I think that's how you spell it)
Converse of Pythagorean Theorem?
The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.
