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Proof of the Pythagorean Theorem

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#1
Dolphin

Consider a right-angled triangle with sides of lengths a, b, and c, where c is the hypotenuse (the side opposite the right angle).

Step 1: Draw a square with side length (a + b). This square can be divided into four congruent right-angled triangles and a smaller square at the center.

Step 2: The area of the larger square is (a + b)^2 since it has side length (a + b).

Step 3: Each of the four right-angled triangles has an area of (1/2)ab since each triangle can be formed by arranging two congruent right-angled triangles with sides a and b.

Step 4: The area of the smaller square at the center is c^2 since it has side length c (the hypotenuse of the right-angled triangle).

Step 5: Since the larger square is made up of the four triangles and the smaller square, we can express its area as the sum of these parts:
(a + b)^2 = 4 * (1/2)ab + c^2

Step 6: Simplify the equation:
(a^2 + 2ab + b^2) = 2ab + c^2

Step 7: Eliminate the 2ab term on both sides:
a^2 + b^2 = c^2

Step 8: This equation shows that the sum of the squares of the two legs (a^2 + b^2) is equal to the square of the hypotenuse (c^2), which is the Pythagorean Theorem.

Therefore, the Pythagorean Theorem is proven. The squares of the lengths of the two legs of a right-angled triangle always add up to the square of the length of the hypotenuse.

#2
Marty
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You're telling me, a heron made this formula?

#7
Dolphin
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no

#3
Manaphy
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Binomial Theorem Clears 🗿

#4
LyCan52
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🫵🤓

#5
Ldiablo69
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👊🤡

#6
LyCan52
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🫵🤡

#8
wing_0001
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Well written

#9
sp0rtsman
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your point is?

#10
Dolphin
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That the pythagorean theorem is true

#11
sp0rtsman
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and?

#12
Dolphin
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it works

#13
sp0rtsman
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so?

#14
Ldiablo69
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So what ?? use it maybe if you need

#15
sp0rtsman
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and then?

#16
Dolphin
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you can use it in your everyday life

#17
sp0rtsman
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for what kind of shit do i need to use it in my everydays life??

#18
Dolphin
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Construction and Carpentry: If you're involved in construction or carpentry, the Pythagorean Theorem is essential for ensuring accurate measurements and right angles. It helps in determining the correct lengths and angles for diagonal supports, roof framing, and checking if walls or corners are perpendicular.

Navigation: The Pythagorean Theorem is fundamental in navigation, particularly for calculating distances. For instance, if you need to find the shortest distance between two points, such as driving from point A to point B directly rather than taking detours, you can use the theorem to calculate the straight-line distance.

Electronics: In electronics and circuit design, the Pythagorean Theorem is used to calculate the magnitude of the total resistance or impedance in a circuit when resistors or components are connected in series or parallel.

Sports and Games: The theorem can be applied in sports like billiards, where players need to calculate angles for bank shots. It's also relevant in games like golf or baseball, where understanding the relationship between distance and angles can help improve strategy and shot selection.

Art and Design: Artists, architects, and designers often use the Pythagorean Theorem to create visually appealing compositions and establish balanced proportions in their work. It helps in determining precise measurements and ensuring harmonious relationships between different elements.

While these are just a few examples, the Pythagorean Theorem demonstrates the relevance of mathematical concepts in practical scenarios. It's always beneficial to have a solid understanding of foundational mathematical principles like this one, as they can have unexpected applications in various aspects of life.

#25
Ic4rusYam2
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ChatGPT

#19
Ldiablo69
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Average American reply

#24
sp0rtsman
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L + im swiss

#23
Dolphin
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also i lied, you dont use it in your everyday life LOL

#20
danii1
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Since I'm too stupid to understand, I agree with you smile

#21
Bobmarlinjr
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Sorry Chat GPT ain’t reading allat

#22
Dolphin
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make an effort

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