Proof: Acute Angles of Right Isosceles Triangle 45

Let's prove the following theorem:

if △XYZ is a right triangle and distance XY = distance YZ, then m∠YZX = 45

X Y Z

Proof:

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Given
1 △XYZ is a right triangle
2 distance XY = distance YZ
Proof Table
# Claim Reason
1 m∠YZX = m∠ZXY if distance XY = distance YZ, then m∠YZX = m∠ZXY
2 (m∠YZX) + (m∠ZXY) = 90 if △XYZ is a right triangle, then (m∠YZX) + (m∠ZXY) = 90
3 (m∠YZX) + (m∠YZX) = 90 if (m∠YZX) + (m∠ZXY) = 90 and m∠YZX = m∠ZXY, then (m∠YZX) + (m∠YZX) = 90
4 m∠YZX = 90 ⋅ (1 / 2) if (m∠YZX) + (m∠YZX) = 90, then m∠YZX = 90 ⋅ (1 / 2)
5 90 ⋅ (1 / 2) = 45 90 ⋅ (1 / 2) = 45
6 m∠YZX = 45 if m∠YZX = 90 ⋅ (1 / 2) and 90 ⋅ (1 / 2) = 45, then m∠YZX = 45

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