Proof: Parallel Then Parallelogram
Let's prove the following theorem:
if AB || CD and DB || CA, then ABDC is a parallelogram
Proof:
Given
| 1 | AB || CD |
|---|---|
| 2 | DB || CA |
| # | Claim | Reason |
|---|---|---|
| 1 | BD || AC | if DB || CA, then BD || AC |
| 2 | AC || BD | if BD || AC, then AC || BD |
| 3 | ABDC is a parallelogram | if AB || CD and AC || BD, then ABDC is a parallelogram |
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