Proof: Exterior Angle Equal to Sum of Nonadjacent
Let's prove the following theorem:
if m∠XYZ = 180, then m∠WYZ = (m∠WXY) + (m∠YWX)
Proof:
Given
1 | m∠XYZ = 180 |
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# | Claim | Reason |
---|---|---|
1 | ((m∠WXY) + (m∠XYW)) + (m∠YWX) = 180 | ((m∠WXY) + (m∠XYW)) + (m∠YWX) = 180 |
2 | (m∠XYW) + (m∠WYZ) = 180 | if m∠XYZ = 180, then (m∠XYW) + (m∠WYZ) = 180 |
3 | (m∠WXY) + (m∠YWX) = 180 + ((m∠XYW) ⋅ (-1)) | if ((m∠WXY) + (m∠XYW)) + (m∠YWX) = 180, then (m∠WXY) + (m∠YWX) = 180 + ((m∠XYW) ⋅ (-1)) |
4 | m∠WYZ = 180 + ((m∠XYW) ⋅ (-1)) | if (m∠XYW) + (m∠WYZ) = 180, then m∠WYZ = 180 + ((m∠XYW) ⋅ (-1)) |
5 | m∠WYZ = (m∠WXY) + (m∠YWX) | if m∠WYZ = 180 + ((m∠XYW) ⋅ (-1)) and (m∠WXY) + (m∠YWX) = 180 + ((m∠XYW) ⋅ (-1)), then m∠WYZ = (m∠WXY) + (m∠YWX) |
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