Question

triangle def is congruent to △def by the sss theorem. which single rigid transformation is required to map △def onto △def? dilation reflection rotation translation

Explanation:

• Dilation: A dilation is a non - rigid transformation (changes the size of the figure). Since the triangles are congruent (same size and shape), dilation is not the answer.
• Reflection: A reflection is a rigid transformation (flips the figure over a line). If we consider a line of reflection (for example, the line \(EF\) or a line perpendicular to \(DD'\) at its mid - point), we can map \(\triangle DEF\) onto \(\triangle D'EF\).
• Rotation: A rotation is a rigid transformation (turns the figure around a point). But in the given figure, there is no indication of a rotational center that would map \(\triangle DEF\) onto \(\triangle D'EF\) directly.
• Translation: A translation is a rigid transformation (slides the figure). But in the given figure, the orientation of the triangles (the position of \(D\) and \(D'\)) is such that a simple slide (translation) will not map \(\triangle DEF\) onto \(\triangle D'EF\).

Answer:

reflection