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

Proof: Diagonal Bisects Rhombus

Let's prove the following theorem:

if WXYZ is a rhombus, then m∠WZX = m∠YZX

Z W X Y P

Proof:

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Given
1 WXYZ is a rhombus
Additional Assumptions
2 m∠WPY = 180
3 m∠XPZ = 180
Proof Table
# Claim Reason
1 △PWX ≅ △PYZ if WXYZ is a rhombus and m∠WPY = 180 and m∠XPZ = 180, then △PWX ≅ △PYZ
2 distance PW = distance PY if △PWX ≅ △PYZ, then distance PW = distance PY
3 distance WZ = distance ZY if WXYZ is a rhombus, then distance WZ = distance ZY
4 distance WZ = distance YZ if distance WZ = distance ZY, then distance WZ = distance YZ
5 distance ZP = distance ZP distance ZP = distance ZP
6 △WZP ≅ △YZP if distance WZ = distance YZ and distance ZP = distance ZP and distance PW = distance PY, then △WZP ≅ △YZP
7 m∠WZP = m∠YZP if △WZP ≅ △YZP, then m∠WZP = m∠YZP
8 m∠WZX = m∠YZX if m∠XPZ = 180 and m∠WZP = m∠YZP, then m∠WZX = m∠YZX
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