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
Proof:
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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