Geometry (Beta) / Chapter 5: Quadrilaterals / The Rhombus

Proof: Sides of Rhombus Congruent 4

Let's prove the following theorem:

if WXYZ is a rhombus, then distance XY = distance YZ

Z W X Y

Proof:

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Given
1 WXYZ is a rhombus
Proof Table
# Claim Reason
1 distance WX = distance XY if WXYZ is a rhombus, then distance WX = distance XY
2 WXYZ is a parallelogram if WXYZ is a rhombus, then WXYZ is a parallelogram
3 distance WX = distance ZY if WXYZ is a parallelogram, then distance WX = distance ZY
4 distance XY = distance ZY if distance WX = distance XY and distance WX = distance ZY, then distance XY = distance ZY
5 distance XY = distance YZ if distance XY = distance ZY, then distance XY = distance YZ
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