Reflection of triangle ABC is nothing but flipping of triangle over a line L.
The triangle ABC is the pre image and the triangle A'B'C' is the image after reflection. D can be any point on the line L.
From the attached figure we can clearly see that
AD = [tex] A_{L} [/tex]D
BD = [tex] B_{L} [/tex]D
CD = [tex] C_{L} [/tex]D
The corresponding angles are equal.
So we can say that A_LD = [tex] B_{L} [/tex]D is not necessarily true.
