Proof: If Equilateral Then Rhombus
Let's prove the following theorem:
if distance WX = distance XY and distance XY = distance YZ and distance YZ = distance ZW, then WXYZ is a rhombus
Proof:
Proof Table
| # | Claim | Reason |
|---|---|---|
| 1 | distance WX = distance YZ | if distance WX = distance XY and distance XY = distance YZ, then distance WX = distance YZ |
| 2 | distance XY = distance ZW | if distance XY = distance YZ and distance YZ = distance ZW, then distance XY = distance ZW |
| 3 | WXYZ is a parallelogram | if distance WX = distance YZ and distance XY = distance ZW, then WXYZ is a parallelogram |
| 4 | WXYZ is a rhombus | if WXYZ is a parallelogram and distance WX = distance XY, then WXYZ is a rhombus |
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