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

Y W X Z

Proof:

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Given
1 WXYZ is a rhombus
2 ∠WXY is a right angle
Proof Table
# 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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