Proof: If Parallelogram Inner Congruent
Let's prove the following theorem:
if WXYZ is a parallelogram and m∠WPY = 180 and m∠XPZ = 180, then △PYZ ≅ △PWX
Proof:
Proof Table
| # | Claim | Reason |
|---|---|---|
| 1 | WX || ZY | if WXYZ is a parallelogram, then WX || ZY |
| 2 | m∠WXZ = m∠XZY | if WX || ZY, then m∠WXZ = m∠XZY |
| 3 | m∠WXZ = m∠YZX | if m∠WXZ = m∠XZY, then m∠WXZ = m∠YZX |
| 4 | m∠YZX = m∠YZP | if m∠XPZ = 180, then m∠YZX = m∠YZP |
| 5 | m∠WXZ = m∠WXP | if m∠XPZ = 180, then m∠WXZ = m∠WXP |
| 6 | m∠YZP = m∠WXP | if m∠WXZ = m∠YZX and m∠YZX = m∠YZP and m∠WXZ = m∠WXP, then m∠YZP = m∠WXP |
| 7 | m∠ZYW = m∠YWX | if WX || ZY, then m∠ZYW = m∠YWX |
| 8 | m∠ZYW = m∠ZYP | if m∠WPY = 180, then m∠ZYW = m∠ZYP |
| 9 | m∠YWX = m∠PWX | if m∠WPY = 180, then m∠YWX = m∠PWX |
| 10 | m∠ZYP = m∠PWX | if m∠ZYW = m∠YWX and m∠ZYW = m∠ZYP and m∠YWX = m∠PWX, then m∠ZYP = m∠PWX |
| 11 | m∠PYZ = m∠PWX | if m∠ZYP = m∠PWX, then m∠PYZ = m∠PWX |
| 12 | distance WX = distance ZY | if WXYZ is a parallelogram, then distance WX = distance ZY |
| 13 | distance YZ = distance WX | if distance WX = distance ZY, then distance YZ = distance WX |
| 14 | △PYZ ≅ △PWX | if m∠PYZ = m∠PWX and distance YZ = distance WX and m∠YZP = m∠WXP, then △PYZ ≅ △PWX |
Comments
Please log in to add comments