K-12 – Geometry – The Pythagorean Theorem

The Pythagoras theorem states that if a triangle is a right-angled triangle, then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC² = AB² + AC². Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle. [1]

Parts of Triangle used for the Proof of Pythagorean Theorem

Pythagoras Theorem Equation

The Pythagoras theorem equation is expressed as, c² = a² + b², where ‘c’ = hypotenuse of the right triangle and ‘a’ and ‘b’ are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle. [1]

History of Pythagoras Theorem

Pythagoras theorem was introduced by the Greek Mathematician Pythagoras of Samos. He was an ancient Greek philosopher who formed a group of mathematicians who worked religiously on numbers and lived like monks. Although Pythagoras introduced the theorem, there is evidence that proves that it existed in other civilizations too, 1000 years before Pythagoras was born. The oldest known evidence is seen between the 20th to the 16th century B.C in the Old Babylonian Period. [1]

References

[1] “Pythagoras Theorem – Formula, Proof, Examples.” 2023. Cuemath. Accessed November 23. https://www.cuemath.com/geometry/pythagoras-theorem/.

Additional Reading

Baker, Steve. “In Your Opinion, What Is the Best Proof of the Pythagorean Theorem?” 2023. Quora. Accessed November 23. https://qr.ae/pKMhnN.

McNulty, Keith. 2023. “Here’s How Two Teenagers Found a New Proof of the Pythagorean Theorem.” Medium. Medium. November 18. https://keith-mcnulty.medium.com/heres-how-two-teenagers-found-a-new-proof-of-the-pythagorean-theorem-4afb36219597.

“Pythagoras Theorem – Formula, Proof, Examples, Applications.” 2023. BYJUS. BYJU’S. June 13. https://byjus.com/maths/pythagoras-theorem/.

Videos

Visualizing Pythagoras Theorem

How many ways are there to prove the Pythagorean theorem?

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