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