Proof: Example 2

Let's prove the following theorem:

if WXYZ is a parallelogram and m∠WSX = 180 and m∠ZTY = 180 and distance WS = distance TY, then ZS || TX

Z W X Y S T

Proof:

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Given
1 WXYZ is a parallelogram
2 m∠WSX = 180
3 m∠ZTY = 180
4 distance WS = distance TY
Proof Table
# Claim Reason
1 distance WX = distance ZY if WXYZ is a parallelogram, then distance WX = distance ZY
2 distance WX = (distance WS) + (distance SX) if m∠WSX = 180, then distance WX = (distance WS) + (distance SX)
3 distance ZY = (distance ZT) + (distance TY) if m∠ZTY = 180, then distance ZY = (distance ZT) + (distance TY)
4 distance SX = distance ZT if distance WX = (distance WS) + (distance SX) and distance ZY = (distance ZT) + (distance TY) and distance WX = distance ZY and distance WS = distance TY, then distance SX = distance ZT
5 WX || ZY if WXYZ is a parallelogram, then WX || ZY
6 SX || ZT if WX || ZY and m∠WSX = 180 and m∠ZTY = 180, then SX || ZT
7 distance SX = distance TZ if distance SX = distance ZT, then distance SX = distance TZ
8 SZ || XT if distance SX = distance TZ and SX || ZT, then SZ || XT
9 ZS || TX if SZ || XT, then ZS || TX

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