Proof: Perpendicular to One Then Other

Let's prove the following theorem:

if WX || YZ and m∠WSX = 180 and m∠YTZ = 180 and WS ⊥ ST, then YT ⊥ TS

W S X Y T Z

Proof:

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

Given
1 WX || YZ
2 m∠WSX = 180
3 m∠YTZ = 180
4 WS ⊥ ST
Proof Table
# Claim Reason
1 m∠WST = 90 if WS ⊥ ST, then m∠WST = 90
2 m∠WST = m∠STZ if WX || YZ and m∠WSX = 180 and m∠YTZ = 180, then m∠WST = m∠STZ
3 m∠STZ = 90 if m∠WST = m∠STZ and m∠WST = 90, then m∠STZ = 90
4 ∠YTS and ∠STZ are supplementary if m∠YTZ = 180, then ∠YTS and ∠STZ are supplementary
5 (m∠YTS) + (m∠STZ) = 180 if ∠YTS and ∠STZ are supplementary, then (m∠YTS) + (m∠STZ) = 180
6 (m∠YTS) + 90 = 180 if (m∠YTS) + (m∠STZ) = 180 and m∠STZ = 90, then (m∠YTS) + 90 = 180
7 m∠YTS = 180 + (90 ⋅ (-1)) if (m∠YTS) + 90 = 180, then m∠YTS = 180 + (90 ⋅ (-1))
8 m∠YTS = 90 if m∠YTS = 180 + (90 ⋅ (-1)), then m∠YTS = 90
9 ∠YTS is a right angle if m∠YTS = 90, then ∠YTS is a right angle
10 YT ⊥ TS if ∠YTS is a right angle, then YT ⊥ TS

Comments

Please log in to add comments