Respuesta :
Answer: Option A i.e. [tex]A_LD=B_LD[/tex] is not necessarily true.
Explanation:
Since, According to the definition of Reflection, If a shape reflected through any line, then ,we get a congruent shape with respect to given shape.
So, If [tex]\triangle ABC[/tex] reflected across a line L and makes [tex]\triangle A_LB_LC_L[/tex] then, [tex]\triangle ABC\cong \triangle A_LB_LC_L[/tex]
Thus, corresponding measurements must be Congruent.( CPCT )
That is, [tex]AB=A_LB_L[/tex], [tex]AC=A_LC_L[/tex], [tex]BC=B_LC_L[/tex],
[tex]\angle BAC=\angle B_LA_LC_L[/tex], [tex]\angle ABC=\angle A_LB_LC_L[/tex] and [tex]\angle ACB=\angle A_LC_LB_L[/tex]
Moreover,The corresponding Distance of vertices from the reflected point D is same for [tex]\triangle ABC[/tex]and [tex]\triangle A_LB_LC_L[/tex]( according to the property of reflection)
That is, [tex]AD=A_LD[/tex] [tex]BD=B_LD[/tex] and [tex]CD=C_LD[/tex]
But, it is not necessary, [tex]AD=B_LD[/tex].
Therefore option first is unnecessary.
