Proof: If Parallelogram Diagonal Then Congruent Triangles
Let's prove the following theorem:
if WXYZ is a parallelogram, then △ZWY ≅ △XYW
Proof:
Given
| 1 | WXYZ is a parallelogram |
|---|
| # | Claim | Reason |
|---|---|---|
| 1 | WX || ZY | if WXYZ is a parallelogram, then WX || ZY |
| 2 | WZ || XY | if WXYZ is a parallelogram, then WZ || XY |
| 3 | m∠XWY = m∠WYZ | if WX || ZY, then m∠XWY = m∠WYZ |
| 4 | m∠WYZ = m∠YWX | if m∠XWY = m∠WYZ, then m∠WYZ = m∠YWX |
| 5 | m∠ZWY = m∠WYX | if WZ || XY, then m∠ZWY = m∠WYX |
| 6 | m∠ZWY = m∠XYW | if m∠ZWY = m∠WYX, then m∠ZWY = m∠XYW |
| 7 | distance WY = distance YW | distance WY = distance YW |
| 8 | △ZWY ≅ △XYW | if m∠ZWY = m∠XYW and distance WY = distance YW and m∠WYZ = m∠YWX, then △ZWY ≅ △XYW |
Comments
Please log in to add comments