Proof: Vertical Angles 2
Let's prove the following theorem:
if m∠WPY = 180 and m∠XPZ = 180, then m∠ZPY = m∠XPW
Proof:
Proof Table
# | Claim | Reason |
---|---|---|
1 | ∠WPZ and ∠ZPY are supplementary | if m∠WPY = 180, then ∠WPZ and ∠ZPY are supplementary |
2 | (m∠WPZ) + (m∠ZPY) = 180 | if ∠WPZ and ∠ZPY are supplementary, then (m∠WPZ) + (m∠ZPY) = 180 |
3 | m∠ZPY = 180 + ((m∠WPZ) ⋅ (-1)) | if (m∠WPZ) + (m∠ZPY) = 180, then m∠ZPY = 180 + ((m∠WPZ) ⋅ (-1)) |
4 | ∠XPW and ∠WPZ are supplementary | if m∠XPZ = 180, then ∠XPW and ∠WPZ are supplementary |
5 | (m∠XPW) + (m∠WPZ) = 180 | if ∠XPW and ∠WPZ are supplementary, then (m∠XPW) + (m∠WPZ) = 180 |
6 | m∠XPW = 180 + ((m∠WPZ) ⋅ (-1)) | if (m∠XPW) + (m∠WPZ) = 180, then m∠XPW = 180 + ((m∠WPZ) ⋅ (-1)) |
7 | m∠ZPY = m∠XPW | if m∠ZPY = 180 + ((m∠WPZ) ⋅ (-1)) and m∠XPW = 180 + ((m∠WPZ) ⋅ (-1)), then m∠ZPY = m∠XPW |
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