Proof: Parallel Then Parallelogram

Let's prove the following theorem:

if AB || CD and DB || CA, then ABDC is a parallelogram

C A B D P

Proof:

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Given
1 AB || CD
2 DB || CA
Proof Table
# 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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