Proof: Triangles Adjacent to Isosceles
Let's prove the following theorem:
if m∠WXY = 180 and m∠XYZ = 180 and distance WX = distance ZY and distance XM = distance YM, then distance WM = distance ZM
Proof:
Proof Table
| # | Claim | Reason |
|---|---|---|
| 1 | m∠YXM = m∠XYM | if distance XM = distance YM, then m∠YXM = m∠XYM |
| 2 | m∠XYM = m∠MXY | if m∠YXM = m∠XYM, then m∠XYM = m∠MXY |
| 3 | ∠WXM and ∠MXY are supplementary | if m∠WXY = 180, then ∠WXM and ∠MXY are supplementary |
| 4 | (m∠WXM) + (m∠MXY) = 180 | if ∠WXM and ∠MXY are supplementary, then (m∠WXM) + (m∠MXY) = 180 |
| 5 | m∠WXM = 180 + ((m∠MXY) ⋅ (-1)) | if (m∠WXM) + (m∠MXY) = 180, then m∠WXM = 180 + ((m∠MXY) ⋅ (-1)) |
| 6 | ∠XYM and ∠MYZ are supplementary | if m∠XYZ = 180, then ∠XYM and ∠MYZ are supplementary |
| 7 | (m∠XYM) + (m∠MYZ) = 180 | if ∠XYM and ∠MYZ are supplementary, then (m∠XYM) + (m∠MYZ) = 180 |
| 8 | (m∠MXY) + (m∠MYZ) = 180 | if (m∠XYM) + (m∠MYZ) = 180 and m∠XYM = m∠MXY, then (m∠MXY) + (m∠MYZ) = 180 |
| 9 | m∠MYZ = 180 + ((m∠MXY) ⋅ (-1)) | if (m∠MXY) + (m∠MYZ) = 180, then m∠MYZ = 180 + ((m∠MXY) ⋅ (-1)) |
| 10 | m∠WXM = m∠MYZ | if m∠WXM = 180 + ((m∠MXY) ⋅ (-1)) and m∠MYZ = 180 + ((m∠MXY) ⋅ (-1)), then m∠WXM = m∠MYZ |
| 11 | m∠WXM = m∠ZYM | if m∠WXM = m∠MYZ, then m∠WXM = m∠ZYM |
| 12 | △WXM ≅ △ZYM | if distance WX = distance ZY and m∠WXM = m∠ZYM and distance XM = distance YM, then △WXM ≅ △ZYM |
| 13 | distance WM = distance ZM | if △WXM ≅ △ZYM, then distance WM = distance ZM |
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