Proof: Perpendicular Then Parallel
Let's prove the following theorem:
if WX ⊥ XS and YZ ⊥ ZT and m∠WXG = 180 and m∠YZH = 180 and m∠SXZ = 180 and m∠XZT = 180, then YH || WG
Proof:
Proof Table
# | Claim | Reason |
---|---|---|
1 | m∠WXS = 90 | if WX ⊥ XS, then m∠WXS = 90 |
2 | m∠YZT = 90 | if YZ ⊥ ZT, then m∠YZT = 90 |
3 | m∠WXS = m∠ZXG | if m∠SXZ = 180 and m∠WXG = 180, then m∠WXS = m∠ZXG |
4 | m∠ZXG = 90 | if m∠WXS = m∠ZXG and m∠WXS = 90, then m∠ZXG = 90 |
5 | ∠XZY and ∠YZT are supplementary | if m∠XZT = 180, then ∠XZY and ∠YZT are supplementary |
6 | (m∠XZY) + (m∠YZT) = 180 | if ∠XZY and ∠YZT are supplementary, then (m∠XZY) + (m∠YZT) = 180 |
7 | (m∠XZY) + 90 = 180 | if (m∠XZY) + (m∠YZT) = 180 and m∠YZT = 90, then (m∠XZY) + 90 = 180 |
8 | m∠XZY = 90 | if (m∠XZY) + 90 = 180, then m∠XZY = 90 |
9 | m∠ZXG = m∠XZY | if m∠ZXG = 90 and m∠XZY = 90, then m∠ZXG = m∠XZY |
10 | YH || WG | if m∠YZH = 180 and m∠WXG = 180 and m∠ZXG = m∠XZY, then YH || WG |
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