Question

determine whether each claim about the properties of △abc and △abc is true or false.
ab and ab are on the same line.
ac and ac are on distinct parallel lines.

Explanation:

Step1: Analyze line - segment AB and A'B'

Without seeing the transformation from △ABC to △A'B'C', if there is a rigid - motion transformation (translation, rotation, reflection), in general, \(\overline{AB}\) and \(\overline{A'B'}\) are not on the same line. They are corresponding line - segments of two different triangles.

Step2: Analyze line - segment AC and A'C'

Similarly, for corresponding line - segments \(\overline{AC}\) and \(\overline{A'C'}\) of two different triangles △ABC and △A'B'C', in most rigid - motion transformations, they are not on distinct parallel lines. A rotation or reflection will not result in \(\overline{AC}\) and \(\overline{A'C'}\) being on parallel lines, and a non - parallel translation will also not make them parallel.

Answer:

1. False
2. False