SOLUTION: Given: Trapezoid WXYZ with bases WX and ZY, Rectangle WXAB, WA perpendicular to ZY XB perpendicular ZY , ZA is congruent to YB Prove:Trapezoid WXYZ is isosceles

Algebra ->  Geometry-proofs -> SOLUTION: Given: Trapezoid WXYZ with bases WX and ZY, Rectangle WXAB, WA perpendicular to ZY XB perpendicular ZY , ZA is congruent to YB Prove:Trapezoid WXYZ is isosceles       Log On


   

Question 585406: Given: Trapezoid WXYZ with bases WX and ZY, Rectangle WXAB, WA perpendicular to ZY
XB perpendicular ZY , ZA is congruent to YB
Prove:Trapezoid WXYZ is isosceles
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Statement Reason
1. WA perpendicular to ZY Given
2. XB perpendicular ZY Given
3. ZA = YB Given
4. < ZAW = < YBX All perpendicular angles equal 90 degrees
5. WA = XB Opposite sides of a rectangle are equal
6. triangle ZAW = triangle YBX SAS property
7. ZW = YX CPCTC
8. trapezoid WXYZ is isosceles nonparallel sides are congruent