Proof: If Isosceles Trapezoid Angles Congruent

Let's prove the following theorem:

if quadrilateral WXYZ is an isosceles trapezoid, then m∠ZWX = m∠WXY

P W X Y Z

Proof:

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Given
1 quadrilateral WXYZ is an isosceles trapezoid
Assumptions
2 WZ || PY
3 m∠WPX = 180
Proof Table
# Claim Reason
1 distance WZ = distance XY if quadrilateral WXYZ is an isosceles trapezoid, then distance WZ = distance XY
2 WX || ZY if quadrilateral WXYZ is an isosceles trapezoid, then WX || ZY
3 WP || ZY if WX || ZY and m∠WPX = 180, then WP || ZY
4 WPYZ is a parallelogram if WP || ZY and WZ || PY, then WPYZ is a parallelogram
5 distance WZ = distance PY if WPYZ is a parallelogram, then distance WZ = distance PY
6 distance PY = distance XY if distance WZ = distance PY and distance WZ = distance XY, then distance PY = distance XY
7 m∠YPX = m∠PXY if distance PY = distance XY, then m∠YPX = m∠PXY
8 YP || ZW if WZ || PY, then YP || ZW
9 m∠XPW = 180 if m∠WPX = 180, then m∠XPW = 180
10 m∠YPX = m∠ZWP if YP || ZW and m∠XPW = 180, then m∠YPX = m∠ZWP
11 m∠ZWP = m∠PXY if m∠YPX = m∠ZWP and m∠YPX = m∠PXY, then m∠ZWP = m∠PXY
12 m∠ZWX = m∠WXY if m∠ZWP = m∠PXY and m∠WPX = 180, then m∠ZWX = m∠WXY

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