Proof: Isosceles Triangle Opposites

Let's prove the following theorem:

if distance ZY = distance ZX, then m∠ZXY = m∠XYZ

X Y Z

Proof:

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Given
1 distance ZY = distance ZX
Proof Table
# Claim Reason
1 distance XZ = distance YZ if distance ZY = distance ZX, then distance XZ = distance YZ
2 m∠YXZ = m∠XYZ if distance XZ = distance YZ, then m∠YXZ = m∠XYZ
3 m∠ZXY = m∠XYZ if m∠YXZ = m∠XYZ, then m∠ZXY = m∠XYZ
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