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Mathematical Theorem: Pythagorean Theorem
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As stated by the Pythagoreans, "In a right-angled triangle, the square of the
hypotenuse side is equal to the sum of squares of the other two sides." In this triangle, the
sides are named Perpendicular, Base, and Hypotenuse. Because it is on the other side of a 90°
angle, the hypotenuse is the side with the greatest length. An equation known as a
Pythagorean triple is created by multiplying the positive integer sides of a right triangle (m, n,
and o) by their squares. Mathematicians use the Pythagorean Theorem to explain how the
sides of a right-angled triangle are related. The Pythagorean triples are the sides of the right
triangle. A triangle's length and angle can be determined using Pythagoras' theorem. The
base, perpendicular, and hypotenuse formulas can all be derived from this theorem.
m
n
In above triangle, “m” is the perpendicular, “n” is the base, “o” is the hypotenuse. As
it states, Hypotenuse ^2 = Base^2 + Perpendicular^2
o^2 = m^2 + n^2. For example, let’s say m= 6 and n= 8. Hence, o^2 = 36 + 64, o= 10.
Proof
Consider the triangle below. Note that this theorem applies only to Right-angled triangles
N
M
3
We know, △MPN ~ △MNO.
Therefore, MP/MN = MN/MO. Or MN2 = MP * MO ………… (1).
Also, △NPO ~ △MNO. Therefore, OP/NO = NO/MO. (similar triangles with corresponding
sides). Or NO2 = OP * MO ………. (2). We then add equations 1 & 2;
MN2 + NO2 = MP * MO + OP * MO.
MN2 + NO2 = MO(MP+OP)
Since, MP + OP = MO, MO2 = MN2 + NO2
Hence proven.
References
Mastin, L. (2020). Pythagorean Theorem – Explanation & Examples. The Story of
Mathematics - a History of Mathematical Thought from Ancient Times to the Modern
Day. https://www.storyofmathematics.com/pythagorean-theorem/
Praneeth. (2021). Pythagoras Theorem - Statement, Formula, Proof and Examples. BYJUS.
https://byjus.com/maths/pythagoras-theorem/
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