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

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• m∠ZWX = m∠WXY, if (m∠DAX = m∠XBC) and (m∠AXB = 180), then m∠DAB = m∠ABC
  • m∠ZWP = m∠PXY,

    if the following are true:

    • a = b
    • a = c

    then b = c

    • m∠YPX = m∠ZWP, if (WX || YZ) and (m∠RXZ = 180), then m∠WXR = m∠YZX
      • YP || ZW, if AB || CD, then DC || BA
        • WZ || PY
      • m∠XPW = 180, if m∠ABC = x, then m∠CBA = x
        • m∠WPX = 180
    • m∠YPX = m∠PXY, if distance XZ = distance YZ, then m∠ZXY = m∠XYZ
      • distance PY = distance XY,

        if the following are true:

        • a = b
        • a = c

        then b = c

        • distance WZ = distance PY, if WXYZ is a parallelogram, then distance WZ = distance XY
          • WPYZ is a parallelogram, if (AB || CD) and (AC || BD), then ABDC is a parallelogram
            • WP || ZY, if (AB || YZ) and (m∠AXB = 180), then AX || YZ
              • WX || ZY, if quadrilateral ABCD is an isosceles trapezoid, then AB || DC
                • quadrilateral WXYZ is an isosceles trapezoid
              • m∠WPX = 180
            • WZ || PY
        • distance WZ = distance XY, if quadrilateral ABCD is an isosceles trapezoid, then distance AD = distance BC
          • quadrilateral WXYZ is an isosceles trapezoid
  • m∠WPX = 180