Proof: Corresponding Angles Then Parallel
Let's prove the following theorem:
if m∠WJI = m∠YKJ and m∠WJX = 180 and m∠YKZ = 180 and m∠IJK = 180, then WX || YZ
Proof:
Proof Table
| # | Claim | Reason |
|---|---|---|
| 1 | m∠WJI = m∠XJK | if m∠WJX = 180 and m∠IJK = 180, then m∠WJI = m∠XJK |
| 2 | m∠YKJ = m∠XJK | if m∠WJI = m∠YKJ and m∠WJI = m∠XJK, then m∠YKJ = m∠XJK |
| 3 | m∠YKJ = m∠JKY | m∠YKJ = m∠JKY |
| 4 | m∠XJK = m∠JKY | if m∠YKJ = m∠XJK and m∠YKJ = m∠JKY, then m∠XJK = m∠JKY |
| 5 | m∠XJW = 180 | if m∠WJX = 180, then m∠XJW = 180 |
| 6 | m∠ZKY = 180 | if m∠YKZ = 180, then m∠ZKY = 180 |
| 7 | WX || YZ | if m∠XJW = 180 and m∠ZKY = 180 and m∠XJK = m∠JKY, then WX || YZ |
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