Transitive Property of Equality Variation 2
Collinear Then 180
Subtract Both Sides
Add Term to Both Sides 6
Subtract Both Sides 2
Add Term to Both Sides 7
Transitive Property of Equality Variation 1
Vertical Angles

Proof: Vertical Angles

Let's prove the following theorem:

if m∠XPW = 180 and m∠YPZ = 180, then m∠WPZ = m∠XPY

W Y Z X P

Proof:

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Given
1 m∠XPW = 180
2 m∠YPZ = 180
Proof Table
# Claim Reason
1 (m∠XPY) + (m∠YPW) = 180 if m∠XPW = 180, then (m∠XPY) + (m∠YPW) = 180
2 m∠XPY = 180 + ((m∠YPW) ⋅ (-1)) if (m∠XPY) + (m∠YPW) = 180, then m∠XPY = 180 + ((m∠YPW) ⋅ (-1))
3 (m∠YPW) + (m∠WPZ) = 180 if m∠YPZ = 180, then (m∠YPW) + (m∠WPZ) = 180
4 m∠WPZ = 180 + ((m∠YPW) ⋅ (-1)) if (m∠YPW) + (m∠WPZ) = 180, then m∠WPZ = 180 + ((m∠YPW) ⋅ (-1))
5 m∠WPZ = m∠XPY if m∠WPZ = 180 + ((m∠YPW) ⋅ (-1)) and m∠XPY = 180 + ((m∠YPW) ⋅ (-1)), then m∠WPZ = m∠XPY
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