ABCD is a square; X is the mid-point of AB and Y the mid-point of BC.Hence, DX is perpendicular to AY.
If the above statement is true then mention answer as 1, else mention 0 if false.
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AB=BC (ABCD is a square) ∴12AB=12BC ∴AX=BY ...(X and Y are mid points of AB and BC respectively) In △AXD and △ABY, ∠DAX=∠ABY (Each 90∘) AX=BY (Proved above) AD=AB (ABCD is a square) Thus, △AXD≅△BYA ....(SAS test) ∠AXD=∠BYA (By cpct)
i.e ∠AXO=∠OYB ...(I) Now, In quadrilateral XOYB, Sum of angles = 360 ∠XOY+∠OYB+∠YBX+∠BXO=360o ∠XOY+∠OYB+90+180−∠AXO=360o But ∠OYB=∠AXO (From I) hence, ∠XOY=90∘ DX⊥AY
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