Question

angle congruence: sss and hl
triangle abc is congruent to △abc by the hl theorem.
what single rigid transformation maps △abc onto △abc?
rotation
reflection
translation
dilation

Explanation:

Step1: Analyze Rigid Transformations

Rigid transformations (translation, rotation, reflection) preserve shape and size. Dilation changes size, so eliminate dilation.

Step2: Check Reflection

A reflection over line \( BB' \) (or the vertical line through \( B \)) would map \( \triangle ABC \) to \( \triangle A'BC' \), as the triangles are mirror images over this line. Translation moves without rotation/reflection, rotation would involve a center, but here the mirroring (reflection) is evident from the symmetric positions over \( B \)'s vertical line.

Step3: Eliminate Other Options

Translation: Triangles aren't shifted, just mirrored. Rotation: No rotational center fits as well as reflection. Dilation: Already eliminated. So reflection is correct.

Answer:

reflection