Question

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

Explanation:

Step1: Recall Rigid Transformations

Rigid transformations (translation, rotation, reflection) preserve shape and size (congruence), while dilation changes size (so not rigid). So eliminate dilation.

Step2: Analyze Translation

Translation moves a figure without rotation/reflection. The triangles here don't look like a simple shift; their orientation relative to vertex \( E \) suggests rotation.

Step3: Analyze Rotation vs Reflection

Looking at the triangles, a rotation about point \( E \) (common vertex) would map \( \triangle DEF \) to \( \triangle D'EF' \). Reflection would flip over a line, but the symmetry here fits rotation (around \( E \)) better.

Answer:

rotation (the option labeled "rotation")