Proof: Supplementary Angles
Let's prove the following theorem:
if m∠AMB = 180, then ∠AMC and ∠BMC are supplementary
Proof:
Given
1 | m∠AMB = 180 |
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# | Claim | Reason |
---|---|---|
1 | ∠AMC and ∠CMB are supplementary | if m∠AMB = 180, then ∠AMC and ∠CMB are supplementary |
2 | (m∠AMC) + (m∠CMB) = 180 | if ∠AMC and ∠CMB are supplementary, then (m∠AMC) + (m∠CMB) = 180 |
3 | m∠CMB = m∠BMC | m∠CMB = m∠BMC |
4 | (m∠AMC) + (m∠BMC) = 180 | if (m∠AMC) + (m∠CMB) = 180 and m∠CMB = m∠BMC, then (m∠AMC) + (m∠BMC) = 180 |
5 | ∠AMC and ∠BMC are supplementary | if (m∠AMC) + (m∠BMC) = 180, then ∠AMC and ∠BMC are supplementary |
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