Proof: Acute Angles of Right Triange Comlementary
Let's prove the following theorem:
if △XYZ is a right triangle, then (m∠YZX) + (m∠ZXY) = 90
Proof:
Given
1 | △XYZ is a right triangle |
---|
# | Claim | Reason |
---|---|---|
1 | m∠XYZ = 90 | if △XYZ is a right triangle, then m∠XYZ = 90 |
2 | ((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 | ((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 |
3 | (90 + (m∠YZX)) + (m∠ZXY) = 180 | if ((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 and m∠XYZ = 90, then (90 + (m∠YZX)) + (m∠ZXY) = 180 |
4 | (m∠YZX) + (m∠ZXY) = 180 + (90 ⋅ (-1)) | if (90 + (m∠YZX)) + (m∠ZXY) = 180, then (m∠YZX) + (m∠ZXY) = 180 + (90 ⋅ (-1)) |
5 | (m∠YZX) + (m∠ZXY) = 90 | if (m∠YZX) + (m∠ZXY) = 180 + (90 ⋅ (-1)), then (m∠YZX) + (m∠ZXY) = 90 |
Comments
Please log in to add comments