Proof: Rearrange Angles
Let's prove the following theorem:
if m∠ACF = (m∠ACG) + (m∠GCF), then m∠FCA = (m∠FCG) + (m∠GCA)
Proof:
Proof Table
# | Claim | Reason |
---|---|---|
1 | m∠FCA = (m∠ACG) + (m∠GCF) | if m∠ACF = (m∠ACG) + (m∠GCF), then m∠FCA = (m∠ACG) + (m∠GCF) |
2 | m∠FCA = (m∠GCF) + (m∠ACG) | if m∠FCA = (m∠ACG) + (m∠GCF), then m∠FCA = (m∠GCF) + (m∠ACG) |
3 | m∠GCF = m∠FCG | m∠GCF = m∠FCG |
4 | m∠FCA = (m∠FCG) + (m∠ACG) | if m∠FCA = (m∠GCF) + (m∠ACG) and m∠GCF = m∠FCG, then m∠FCA = (m∠FCG) + (m∠ACG) |
5 | m∠ACG = m∠GCA | m∠ACG = m∠GCA |
6 | m∠FCA = (m∠FCG) + (m∠GCA) | if m∠FCA = (m∠FCG) + (m∠ACG) and m∠ACG = m∠GCA, then m∠FCA = (m∠FCG) + (m∠GCA) |
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