Alternate Interior Angles Theorem

if m∠WSX = 180 and m∠YTZ = 180 and m∠WST = m∠STZ, then WX || YZ

This is a proof by contradiction

Given(s)


Contradiction
Assumption
1 line WX intersects line YZ at point P
2 m∠WSX = 180
3 m∠YTZ = 180
Proof Table
# Claim Reason
1 m∠WPX = 180 if line WX intersects line YZ at point P, then m∠WPX = 180
2 m∠WSP = 180 if m∠WSX = 180 and m∠WPX = 180, then m∠WSP = 180
3 m∠YPZ = 180 if line WX intersects line YZ at point P, then m∠YPZ = 180
4 m∠TPZ = 180 if m∠YTZ = 180 and m∠YPZ = 180, then m∠TPZ = 180
5 m∠WST > m∠STP if m∠WSP = 180, then m∠WST > m∠STP
6 m∠STP = m∠STZ if m∠TPZ = 180, then m∠STP = m∠STZ
7 m∠WST > m∠STZ if m∠WST > m∠STP and m∠STP = m∠STZ, then m∠WST > m∠STZ
The last statement (m∠WST > m∠STZ) contradicts a given statement


Conclusion

WX || YZ

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