Alternate Interior Angles Theorem (Converse)

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

This is a proof by contradiction

Given(s)

  • WX || YZ

Contradiction
Assumption
1 m∠YTZ = 180
Additional Assumptions
2 m∠HST = m∠STZ
3 m∠HSI = 180
4 line HI intersects line WX at point S
Proof Table
# Claim Reason
1 HI || YZ if m∠HSI = 180 and m∠YTZ = 180 and m∠HST = m∠STZ, then HI || YZ
2 line WX intersects line YZ at point X if HI || YZ and line HI intersects line WX at point S, then line WX intersects line YZ at point X
The last statement (line WX intersects line YZ at point X) contradicts a given statement


Conclusion

m∠WST = m∠STZ

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