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
Proof:
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 |
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