Proof: Diagonal Bisects Rhombus
Let's prove the following theorem:
if WXYZ is a rhombus, then m∠WZX = m∠YZX
Proof:
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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