Proof: Triangles Inside Rhombus
Let's prove the following theorem:
if WXYZ is a rhombus and m∠WPY = 180 and m∠XPZ = 180, then △PWX ≅ △PYZ
Proof:
Proof Table
| # | Claim | Reason |
|---|---|---|
| 1 | WXYZ is a parallelogram | if WXYZ is a rhombus, then WXYZ is a parallelogram |
| 2 | WX || ZY | if WXYZ is a parallelogram, then WX || ZY |
| 3 | m∠ZYW = m∠YWX | if WX || ZY, then m∠ZYW = m∠YWX |
| 4 | m∠ZYP = m∠PWX | if m∠WPY = 180 and m∠ZYW = m∠YWX, then m∠ZYP = m∠PWX |
| 5 | m∠PWX = m∠PYZ | if m∠ZYP = m∠PWX, then m∠PWX = m∠PYZ |
| 6 | m∠YZX = m∠ZXW | if WX || ZY, then m∠YZX = m∠ZXW |
| 7 | m∠YZP = m∠PXW | if m∠XPZ = 180 and m∠YZX = m∠ZXW, then m∠YZP = m∠PXW |
| 8 | m∠WXP = m∠YZP | if m∠YZP = m∠PXW, then m∠WXP = m∠YZP |
| 9 | distance WX = distance ZY | if WXYZ is a parallelogram, then distance WX = distance ZY |
| 10 | distance WX = distance YZ | if distance WX = distance ZY, then distance WX = distance YZ |
| 11 | △PWX ≅ △PYZ | if m∠PWX = m∠PYZ and distance WX = distance YZ and m∠WXP = m∠YZP, then △PWX ≅ △PYZ |
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