Question

ABCD is a square. X is the midpoint of AB, Y is the midpoint of BC. prove DX perpendicular to AY​

Answer 1

Answer:

Step-by-step explanation:

AB=BC (ABCD is a square)

∴  

2

1

​  

AB=  

2

1

​  

BC

∴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=360  

o

 

∠XOY+∠OYB+90+180−∠AXO=360  

o

 

But ∠OYB=∠AXO (From I)

hence, ∠XOY=90  

∘

 

DX⊥AY