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

W X G Y Z H S T

Proof:

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

Given
1 WX ⊥ XS
2 YZ ⊥ ZT
3 m∠WXG = 180
4 m∠YZH = 180
5 m∠SXZ = 180
6 m∠XZT = 180
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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