Question

in the given figure, triangle ABC is congruent to triangle EDA. If X and Y are points lying on AD and EG respectively such that AX/XC =EY/YG=1. The value of DX/FY is always
1. >1
2. =1
3. <1
4. =3/2​

Answer 1

<EGF = <DGC = 90° - <C

<E = <A = 90° - <C

<E = <EGF = >EF = FG

FY is the median in the triangle FEG

FY is the perpendicular to ED

FE // AC (this is the equation 1)

Join BX

BX is the median of triangle ABC

BX = 1/2 AC = XC

<XBC = <C = DAE

ABFX is cyclic quadrilateral

<<AXF = 180° - <ABF = 90°

FX is perpendicular to AC (this equation will be 2)

so from equation 1 and 2

DXFY is a rectangle  = DX = FY

DX/FY = 1

$\pmb{\red{\mathfrak{\underline{\bigstar{Hope \: it \: helps \: \: uh!!}}}}}$

Answer 2

Answer:

<EGF = <DGC = 90° - <C

<E = <A = 90° - <C

<E = <EGF = >EF = FG

FY is the median in the triangle FEG

FY is the perpendicular to ED

FE // AC (this is the equation 1)

Join BX

BX is the median of triangle ABC

BX = 1/2 AC = XC

<XBC = <C = DAE

ABFX is cyclic quadrilateral

<<AXF = 180° - <ABF = 90°

FX is perpendicular to AC (this equation will be 2)

so from equation 1 and 2

DXFY is a rectangle = DX = FY

DX/FY = 1