Question

6. ABCD is a square. L is the mid-point of side AB and M is the
mid-point of side BC. Prove that:
(i) AADL = ABAM
(ii) ZDLA = ZAMB​

Answer 1

Answer:

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