Question

what single rigid transformation maps \\( \triangle abc \\) onto \\( \triangle ab c \\)?
translation
rotation
reflection
dilation

Explanation:

Step1: Understand rigid transformations

Translation moves a figure without rotation or reflection. Rotation turns a figure around a point. Reflection flips a figure over a line. Dilation changes the size (not a rigid transformation).

Step2: Analyze the triangles

Looking at \(\triangle ABC\) and \(\triangle A'BC'\), we can observe that if we consider line \(BC\) (and \(BC'\)) as a reference. A reflection over the line that is the perpendicular bisector of \(CC'\) (or equivalently, a reflection over the line \(BB\) - since \(B\) is a common vertex and the triangles are symmetric with respect to the line passing through \(B\) and perpendicular to \(CC'\)) will map \(\triangle ABC\) onto \(\triangle A'BC'\). A translation would move the figure without creating the mirror - like image. A rotation would require a center of rotation and an angle of rotation, but there is no indication of a rotational center (other than \(B\), but rotation about \(B\) would not map the right - angles and the sides in the correct orientation as in a reflection).

Answer:

reflection