Proof: Pythagorean Theorem 2
Let's prove the following theorem:
if ∠CAB is a right angle, then (distance BC) ⋅ (distance BC) = ((distance AB) ⋅ (distance AB)) + ((distance AC) ⋅ (distance AC))
Proof:
Given
1 | ∠CAB is a right angle |
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# | Claim | Reason |
---|---|---|
1 | ((distance AB) ⋅ (distance AB)) + ((distance AC) ⋅ (distance AC)) = (distance BC) ⋅ (distance BC) | if ∠CAB is a right angle, then ((distance AB) ⋅ (distance AB)) + ((distance AC) ⋅ (distance AC)) = (distance BC) ⋅ (distance BC) |
2 | (distance BC) ⋅ (distance BC) = ((distance AB) ⋅ (distance AB)) + ((distance AC) ⋅ (distance AC)) | if ((distance AB) ⋅ (distance AB)) + ((distance AC) ⋅ (distance AC)) = (distance BC) ⋅ (distance BC), then (distance BC) ⋅ (distance BC) = ((distance AB) ⋅ (distance AB)) + ((distance AC) ⋅ (distance AC)) |
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