Proof: Supplementary Angles

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	∠AMC and ∠CMB are supplementary	if m∠AMB = 180, then ∠AMC and ∠CMB are supplementary (Supplementary Angles Theorem (Converse))
2	(m∠AMC) + (m∠CMB) = 180	if ∠AMC and ∠CMB are supplementary, then (m∠AMC) + (m∠CMB) = 180 (Supplementary Angles Property)
3	m∠CMB = m∠BMC	m∠CMB = m∠BMC (Angle Symmetry Property)
4	(m∠AMC) + (m∠BMC) = 180	if (m∠AMC) + (m∠CMB) = 180 and m∠CMB = m∠BMC, then (m∠AMC) + (m∠BMC) = 180 (Substitution Example 10)
5	∠AMC and ∠BMC are supplementary	if (m∠AMC) + (m∠BMC) = 180, then ∠AMC and ∠BMC are supplementary (Supplementary Angles Property (Converse))

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