Proof: Equilateral Triangle 60
Let's prove the following theorem:
if △XYZ is an equilateral triangle, then m∠XYZ = 60
Proof:
Given
1 | △XYZ is an equilateral triangle |
---|
# | Claim | Reason |
---|---|---|
1 | m∠XYZ = m∠YZX | if △XYZ is an equilateral triangle, then m∠XYZ = m∠YZX |
2 | m∠YZX = m∠ZXY | if △XYZ is an equilateral triangle, then m∠YZX = m∠ZXY |
3 | m∠XYZ = m∠ZXY | if m∠XYZ = m∠YZX and m∠YZX = m∠ZXY, then m∠XYZ = m∠ZXY |
4 | ((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 | ((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 |
5 | ((m∠XYZ) + (m∠YZX)) + (m∠XYZ) = 180 | if ((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 and m∠XYZ = m∠ZXY, then ((m∠XYZ) + (m∠YZX)) + (m∠XYZ) = 180 |
6 | (m∠XYZ) + (m∠YZX) = (m∠XYZ) + (m∠XYZ) | if m∠XYZ = m∠YZX, then (m∠XYZ) + (m∠YZX) = (m∠XYZ) + (m∠XYZ) |
7 | ((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = 180 | if ((m∠XYZ) + (m∠YZX)) + (m∠XYZ) = 180 and (m∠XYZ) + (m∠YZX) = (m∠XYZ) + (m∠XYZ), then ((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = 180 |
8 | ((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = (m∠XYZ) ⋅ 3 | ((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = (m∠XYZ) ⋅ 3 |
9 | (m∠XYZ) ⋅ 3 = 180 | if ((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = (m∠XYZ) ⋅ 3 and ((m∠XYZ) + (m∠XYZ)) + (m∠XYZ) = 180, then (m∠XYZ) ⋅ 3 = 180 |
10 | m∠XYZ = 180 / 3 | if (m∠XYZ) ⋅ 3 = 180, then m∠XYZ = 180 / 3 |
11 | 180 / 3 = 60 | 180 / 3 = 60 |
12 | m∠XYZ = 60 | if m∠XYZ = 180 / 3 and 180 / 3 = 60, then m∠XYZ = 60 |
Comments
Please log in to add comments