Proof: Consecutive Interior Angles Theorem

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(m∠WST) + (m∠YTS) = 180	if ∠WST and ∠YTS are supplementary, then (m∠WST) + (m∠YTS) = 180 (Supplementary Angles Property)
2	m∠YTS = 180 + ((m∠WST) ⋅ (-1))	if (m∠WST) + (m∠YTS) = 180, then m∠YTS = 180 + ((m∠WST) ⋅ (-1)) (Add Term to Both Sides 7)
3	∠WST and ∠TSX are supplementary	if m∠WSX = 180, then ∠WST and ∠TSX are supplementary (Supplementary Angles Theorem (Converse))
4	(m∠WST) + (m∠TSX) = 180	if ∠WST and ∠TSX are supplementary, then (m∠WST) + (m∠TSX) = 180 (Supplementary Angles Property)
5	m∠TSX = 180 + ((m∠WST) ⋅ (-1))	if (m∠WST) + (m∠TSX) = 180, then m∠TSX = 180 + ((m∠WST) ⋅ (-1)) (Add Term to Both Sides 7)
6	m∠YTS = m∠TSX	if m∠YTS = 180 + ((m∠WST) ⋅ (-1)) and m∠TSX = 180 + ((m∠WST) ⋅ (-1)), then m∠YTS = m∠TSX (Transitive Property of Equality Variation 1)
7	WX || YZ	if m∠WSX = 180 and m∠YTZ = 180 and m∠YTS = m∠TSX, then WX || YZ (Alternate Interior Angles Theorem 3)
8	WS || YT	if WX || YZ and m∠WSX = 180 and m∠YTZ = 180, then WS || YT (Parallel Lines Property)

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