Proof: Three Angles
Let's prove the following theorem:
if the following are true:
- 60 + (a ⋅ 2) = 180
- not (2 = 0)
then a = 60
Proof:
Given
| 1 | 60 + (a ⋅ 2) = 180 |
|---|---|
| 2 | not (2 = 0) |
| # | Claim | Reason |
|---|---|---|
| 1 | a ⋅ 2 = 180 + (60 ⋅ (-1)) | if 60 + (a ⋅ 2) = 180, then a ⋅ 2 = 180 + (60 ⋅ (-1)) |
| 2 | 180 + (60 ⋅ (-1)) = 120 | 180 + (60 ⋅ (-1)) = 120 |
| 3 | a ⋅ 2 = 120 | if 180 + (60 ⋅ (-1)) = 120 and a ⋅ 2 = 180 + (60 ⋅ (-1)), then a ⋅ 2 = 120 |
| 4 | a = 120 / 2 | if not (2 = 0) and a ⋅ 2 = 120, then a = 120 / 2 |
| 5 | 120 / 2 = 60 | 120 / 2 = 60 |
| 6 | a = 60 | if 120 / 2 = 60 and a = 120 / 2, then a = 60 |
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