Proof: If Sides Congruent Then Parallelogram
Let's prove the following theorem:
if distance WX = distance YZ and distance WZ = distance XY, then XWZY is a parallelogram
Proof:
Proof Table
| # | Claim | Reason |
|---|---|---|
| 1 | distance XY = distance ZW | if distance WZ = distance XY, then distance XY = distance ZW |
| 2 | distance YW = distance WY | distance YW = distance WY |
| 3 | △WXY ≅ △YZW | if distance WX = distance YZ and distance XY = distance ZW and distance YW = distance WY, then △WXY ≅ △YZW |
| 4 | m∠XWY = m∠WYZ | if △WXY ≅ △YZW, then m∠XWY = m∠WYZ |
| 5 | XW || YZ | if m∠XWY = m∠WYZ, then XW || YZ |
| 6 | m∠ZWY = m∠WYX | if △WXY ≅ △YZW, then m∠ZWY = m∠WYX |
| 7 | ZW || YX | if m∠ZWY = m∠WYX, then ZW || YX |
| 8 | XWZY is a parallelogram | if XW || YZ and ZW || YX, then XWZY is a parallelogram |
Comments
Please log in to add comments