Proof: Rhombus With Right Angle is Square
Let's prove the following theorem:
if WXYZ is a rhombus and ∠WXY is a right angle, then WXYZ is a square
Proof:
Given
| 1 | WXYZ is a rhombus |
|---|---|
| 2 | ∠WXY is a right angle |
| # | Claim | Reason |
|---|---|---|
| 1 | WXYZ is a parallelogram | if WXYZ is a rhombus, then WXYZ is a parallelogram |
| 2 | WXYZ is a rectangle | if WXYZ is a parallelogram and ∠WXY is a right angle, then WXYZ is a rectangle |
| 3 | distance WX = distance XY | if WXYZ is a rhombus, then distance WX = distance XY |
| 4 | WXYZ is a square | if WXYZ is a rectangle and distance WX = distance XY, then WXYZ is a square |
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