Proof: Two of Three Lines Parallel
Let's prove the following theorem:
if WX || LM and YZ || LM and m∠WSX = 180 and m∠YTZ = 180 and m∠LRM = 180 and m∠STR = 180, then WX || YZ
Proof:
Proof Table
# | Claim | Reason |
---|---|---|
1 | m∠WSR = m∠SRM | if WX || LM and m∠WSX = 180 and m∠LRM = 180, then m∠WSR = m∠SRM |
2 | m∠YTR = m∠TRM | if YZ || LM and m∠YTZ = 180 and m∠LRM = 180, then m∠YTR = m∠TRM |
3 | m∠TRM = m∠SRM | if m∠STR = 180, then m∠TRM = m∠SRM |
4 | m∠YTR = m∠SRM | if m∠YTR = m∠TRM and m∠TRM = m∠SRM, then m∠YTR = m∠SRM |
5 | m∠WSR = m∠YTR | if m∠WSR = m∠SRM and m∠YTR = m∠SRM, then m∠WSR = m∠YTR |
6 | m∠WST = m∠WSR | if m∠STR = 180, then m∠WST = m∠WSR |
7 | m∠WST = m∠YTR | if m∠WST = m∠WSR and m∠WSR = m∠YTR, then m∠WST = m∠YTR |
8 | WX || YZ | if m∠WST = m∠YTR and m∠YTZ = 180 and m∠WSX = 180 and m∠STR = 180, then WX || YZ |
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