Pytagorean Theorem Proof
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Pythagorean Theorem: PROOF For any right triangle
abc, a2 + b2 = c2
_____________________________________________________________________________ 1 a
A = a2
2 b
a
b a
A = ab
a
a A = 1/2 ba c
b c
A = c2 A = b2
1. Find the Area of the squares in terms of their internal polygons. 𝐴1𝑡𝑜𝑡 = 𝑎2 + 2𝑎𝑏 + 𝑏 2
𝐴2𝑡𝑜𝑡 = 4
1 2
𝑎𝑏 + 𝑐 2
2. Set the two equations equal to each other, as they are. 𝐴1𝑡𝑜𝑡 = 𝐴2𝑡𝑜𝑡 1 𝑎2 + 2𝑎𝑏 + 𝑏 2 = 4 𝑎𝑏 + 𝑐 2 2
3. Solve for c2. 𝑎2 + 2𝑎𝑏 + 𝑏 2 = 2𝑎𝑏 + 𝑐 2 −2𝑎𝑏
− 2𝑎𝑏
Pythagorean Theorem 𝑎2 + 𝑏 2 = 𝑐 2
Proof Complete.
-Sgt Ryals, USMC
abc, a2 + b2 = c2
_____________________________________________________________________________ 1 a
A = a2
2 b
a
b a
A = ab
a
a A = 1/2 ba c
b c
A = c2 A = b2
1. Find the Area of the squares in terms of their internal polygons. 𝐴1𝑡𝑜𝑡 = 𝑎2 + 2𝑎𝑏 + 𝑏 2
𝐴2𝑡𝑜𝑡 = 4
1 2
𝑎𝑏 + 𝑐 2
2. Set the two equations equal to each other, as they are. 𝐴1𝑡𝑜𝑡 = 𝐴2𝑡𝑜𝑡 1 𝑎2 + 2𝑎𝑏 + 𝑏 2 = 4 𝑎𝑏 + 𝑐 2 2
3. Solve for c2. 𝑎2 + 2𝑎𝑏 + 𝑏 2 = 2𝑎𝑏 + 𝑐 2 −2𝑎𝑏
− 2𝑎𝑏
Pythagorean Theorem 𝑎2 + 𝑏 2 = 𝑐 2
Proof Complete.
-Sgt Ryals, USMC
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