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 |
Comments
Please log in to add comments