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
Proof:
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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