Geometry (Beta) / Chapter 5: Quadrilaterals / Rectangles

Proof: Interior Angles Then Rectangle

Let's prove the following theorem:

if WXYZ is a parallelogram and m∠YZW = m∠ZWX, then WXYZ is a rectangle

Z W X Y

Proof:

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Given
1 WXYZ is a parallelogram
2 m∠YZW = m∠ZWX
Proof Table
# Claim Reason
1 WX || ZY if WXYZ is a parallelogram, then WX || ZY
2 XW || YZ if WX || ZY, then XW || YZ
3 YZ || XW if XW || YZ, then YZ || XW
4 ∠YZW and ∠ZWX are supplementary if YZ || XW, then ∠YZW and ∠ZWX are supplementary
5 (m∠YZW) + (m∠ZWX) = 180 if ∠YZW and ∠ZWX are supplementary, then (m∠YZW) + (m∠ZWX) = 180
6 (m∠YZW) + (m∠YZW) = 180 if (m∠YZW) + (m∠ZWX) = 180 and m∠YZW = m∠ZWX, then (m∠YZW) + (m∠YZW) = 180
7 m∠YZW = 90 if (m∠YZW) + (m∠YZW) = 180, then m∠YZW = 90
8 ∠YZW is a right angle if m∠YZW = 90, then ∠YZW is a right angle
9 WXYZ is a rectangle if WXYZ is a parallelogram and ∠YZW is a right angle, then WXYZ is a rectangle
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