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
- m∠WSX = 180
- m∠YTZ = 180
Contradiction
Assumption
Additional Assumptions
| 1 | m∠YTZ = 180 |
|---|
| 2 | m∠HST = m∠STZ |
|---|---|
| 3 | m∠HSI = 180 |
| 4 | line HI intersects line WX at point S |
| # | 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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