Proof: Outer Triangle Theorem
Let's prove the following theorem:
if distance XZ = distance YZ and m∠XYP = 180, then distance ZP > distance ZX
Proof:
Proof Table
# | Claim | Reason |
---|---|---|
1 | m∠YXZ = m∠XYZ | if distance XZ = distance YZ, then m∠YXZ = m∠XYZ |
2 | m∠ZYX = m∠YXZ | if m∠YXZ = m∠XYZ, then m∠ZYX = m∠YXZ |
3 | m∠ZYX > m∠ZPY | if m∠XYP = 180, then m∠ZYX > m∠ZPY |
4 | m∠YXZ > m∠ZPY | if m∠ZYX > m∠ZPY and m∠ZYX = m∠YXZ, then m∠YXZ > m∠ZPY |
5 | m∠ZXY > m∠ZPY | if m∠YXZ > m∠ZPY, then m∠ZXY > m∠ZPY |
6 | m∠ZXP > m∠ZPX | if m∠ZXY > m∠ZPY and m∠XYP = 180, then m∠ZXP > m∠ZPX |
7 | distance ZP > distance ZX | if m∠ZXP > m∠ZPX, then distance ZP > distance ZX |
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