Proof: If Equiangular Then Rectangle

Let's prove the following theorem:

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

Z W X Y

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 m∠WXY = m∠XYZ
2 m∠XYZ = m∠YZW
3 m∠YZW = m∠ZWX
Proof Table
# Claim Reason
1 m∠WXY = m∠YZW if m∠WXY = m∠XYZ and m∠XYZ = m∠YZW, then m∠WXY = m∠YZW
2 m∠XYZ = m∠ZWX if m∠XYZ = m∠YZW and m∠YZW = m∠ZWX, then m∠XYZ = m∠ZWX
3 WXYZ is a parallelogram if m∠XYZ = m∠ZWX and m∠WXY = m∠YZW, then WXYZ is a parallelogram
4 quadrilateral WXYZ is convex if m∠WXY = m∠YZW and m∠XYZ = m∠ZWX, then quadrilateral WXYZ is convex
5 (((m∠WXY) + (m∠XYZ)) + (m∠YZW)) + (m∠ZWX) = 360 if quadrilateral WXYZ is convex, then (((m∠WXY) + (m∠XYZ)) + (m∠YZW)) + (m∠ZWX) = 360
6 m∠WXY = m∠ZWX if m∠WXY = m∠XYZ and m∠XYZ = m∠ZWX, then m∠WXY = m∠ZWX
7 (((m∠WXY) + (m∠XYZ)) + (m∠YZW)) + (m∠WXY) = 360 if (((m∠WXY) + (m∠XYZ)) + (m∠YZW)) + (m∠ZWX) = 360 and m∠WXY = m∠ZWX, then (((m∠WXY) + (m∠XYZ)) + (m∠YZW)) + (m∠WXY) = 360
8 m∠YZW = m∠WXY if m∠WXY = m∠YZW, then m∠YZW = m∠WXY
9 (((m∠WXY) + (m∠XYZ)) + (m∠WXY)) + (m∠WXY) = 360 if m∠YZW = m∠WXY and (((m∠WXY) + (m∠XYZ)) + (m∠YZW)) + (m∠WXY) = 360, then (((m∠WXY) + (m∠XYZ)) + (m∠WXY)) + (m∠WXY) = 360
10 (m∠WXY) + (m∠XYZ) = (m∠WXY) + (m∠WXY) if m∠WXY = m∠XYZ, then (m∠WXY) + (m∠XYZ) = (m∠WXY) + (m∠WXY)
11 (((m∠WXY) + (m∠WXY)) + (m∠WXY)) + (m∠WXY) = 360 if (((m∠WXY) + (m∠XYZ)) + (m∠WXY)) + (m∠WXY) = 360 and (m∠WXY) + (m∠XYZ) = (m∠WXY) + (m∠WXY), then (((m∠WXY) + (m∠WXY)) + (m∠WXY)) + (m∠WXY) = 360
12 m∠WXY = 90 if (((m∠WXY) + (m∠WXY)) + (m∠WXY)) + (m∠WXY) = 360, then m∠WXY = 90
13 ∠WXY is a right angle if m∠WXY = 90, then ∠WXY is a right angle
14 WXYZ is a rectangle if WXYZ is a parallelogram and ∠WXY is a right angle, then WXYZ is a rectangle

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