Proof: Altitudes Isosceles
Let's prove the following theorem:
if distance YX = distance YZ and XT ⊥ TZ and ZS ⊥ SX and m∠XSY = 180 and m∠ZTY = 180, then distance ZS = distance XT
Proof:
Proof Table
| # | Claim | Reason |
|---|---|---|
| 1 | m∠YXZ = m∠YZX | if distance YX = distance YZ, then m∠YXZ = m∠YZX |
| 2 | m∠SXZ = m∠YXZ | if m∠XSY = 180, then m∠SXZ = m∠YXZ |
| 3 | m∠TZX = m∠YZX | if m∠ZTY = 180, then m∠TZX = m∠YZX |
| 4 | m∠SXZ = m∠YZX | if m∠SXZ = m∠YXZ and m∠YXZ = m∠YZX, then m∠SXZ = m∠YZX |
| 5 | m∠SXZ = m∠TZX | if m∠SXZ = m∠YZX and m∠TZX = m∠YZX, then m∠SXZ = m∠TZX |
| 6 | m∠ZSX = 90 | if ZS ⊥ SX, then m∠ZSX = 90 |
| 7 | m∠XTZ = 90 | if XT ⊥ TZ, then m∠XTZ = 90 |
| 8 | m∠ZSX = m∠XTZ | if m∠ZSX = 90 and m∠XTZ = 90, then m∠ZSX = m∠XTZ |
| 9 | distance XZ = distance ZX | distance XZ = distance ZX |
| 10 | △SXZ ≅ △TZX | if m∠ZSX = m∠XTZ and m∠SXZ = m∠TZX and distance XZ = distance ZX, then △SXZ ≅ △TZX |
| 11 | distance ZS = distance XT | if △SXZ ≅ △TZX, then distance ZS = distance XT |
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