Proof: Angle a Greater Than Angle B

Let's prove the following theorem:

if m∠CAB > m∠CDB and m∠ABD = 180, then m∠CAD > m∠CDA

A B D C

Proof:

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Given
1 m∠CAB > m∠CDB
2 m∠ABD = 180
Proof Table
# Claim Reason
1 m∠CAB = m∠CAD if m∠ABD = 180, then m∠CAB = m∠CAD
2 m∠CAD > m∠CDB if m∠CAB > m∠CDB and m∠CAB = m∠CAD, then m∠CAD > m∠CDB
3 m∠CDB = m∠CDA if m∠ABD = 180, then m∠CDB = m∠CDA
4 m∠CAD > m∠CDA if m∠CAD > m∠CDB and m∠CDB = m∠CDA, then m∠CAD > m∠CDA

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