First of all, AD is congruent to segment AC because the reflection is a rigid transformation. A rigid transformation is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. The rigid transformations include rotations, translations, reflections, or any sequence of these.
Therefore if we reflect △ABC across AB, the new triangle △ABD will be congruent to the triangle △ABC:
[tex]\Delta ABC\cong\Delta ABD[/tex]
By CPCTC theorem, corresponding parts of congruent triangles are congruent
Answer:
Corresponding parts of congruent figures are congruent
