Proof: Lengths Unequal Then Angles Flipped

Let's prove the following theorem:

if distance YZ < distance XY, then m∠YXZ < m∠XZY

Z X Y

Proof:

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Given
1 distance YZ < distance XY
Proof Table
# Claim Reason
1 distance XY > distance YZ if distance YZ < distance XY, then distance XY > distance YZ
2 m∠XZY > m∠YXZ if distance XY > distance YZ, then m∠XZY > m∠YXZ
3 m∠YXZ < m∠XZY if m∠XZY > m∠YXZ, then m∠YXZ < m∠XZY

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