Proof: Rectangle Right Angles 3
Let's prove the following theorem:
if WXYZ is a rectangle, then ∠YZW is a right angle
Proof:
Given
| 1 | WXYZ is a rectangle |
|---|
| # | Claim | Reason |
|---|---|---|
| 1 | WXYZ is a parallelogram | if WXYZ is a rectangle, then WXYZ is a parallelogram |
| 2 | WZ || XY | if WXYZ is a parallelogram, then WZ || XY |
| 3 | ∠XYZ is a right angle | if WXYZ is a rectangle, then ∠XYZ is a right angle |
| 4 | ∠WZY and ∠ZYX are supplementary | if WZ || XY, then ∠WZY and ∠ZYX are supplementary |
| 5 | (m∠WZY) + (m∠ZYX) = 180 | if ∠WZY and ∠ZYX are supplementary, then (m∠WZY) + (m∠ZYX) = 180 |
| 6 | m∠XYZ = 90 | if ∠XYZ is a right angle, then m∠XYZ = 90 |
| 7 | m∠ZYX = m∠XYZ | m∠ZYX = m∠XYZ |
| 8 | m∠ZYX = 90 | if m∠ZYX = m∠XYZ and m∠XYZ = 90, then m∠ZYX = 90 |
| 9 | (m∠WZY) + 90 = 180 | if (m∠WZY) + (m∠ZYX) = 180 and m∠ZYX = 90, then (m∠WZY) + 90 = 180 |
| 10 | m∠WZY = 90 | if (m∠WZY) + 90 = 180, then m∠WZY = 90 |
| 11 | m∠YZW = 90 | if m∠WZY = 90, then m∠YZW = 90 |
| 12 | ∠YZW is a right angle | if m∠YZW = 90, then ∠YZW is a right angle |
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