Question

When triangle ABC is reflected across line AB, the image is triangle ABD. Why are segments AD and segment AC congruent?

Answer 1

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:

`\Delta ABC\cong\Delta ABD`

By CPCTC theorem, corresponding parts of congruent triangles are congruent

Answer:

Corresponding parts of congruent figures are congruent