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

W S X Y T Z L M R

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 WX || LM
2 YZ || LM
3 m∠WSX = 180
4 m∠YTZ = 180
5 m∠LRM = 180
6 m∠STR = 180
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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