Question

a. how can you decide if $\triangle def \cong \triangle def$?
b. is $\triangle def \cong \triangle def$? explain.
a. choose the correct answer below.
a. decide whether a sequence of reflections maps $\triangle def$ to $\triangle def$.
b. decide whether a sequence of translations maps $\triangle def$ to $\triangle def$.
c. decide whether a sequence of transformations maps $\triangle def$ to $\triangle def$.
d. decide whether a sequence of rotations maps $\triangle def$ to $\triangle def$.

Explanation:

To determine if two triangles are congruent, we can check if a sequence of rigid transformations (reflections, translations, rotations) maps one triangle to the other. The key is that rigid transformations preserve the shape and size, so if such a sequence exists, the triangles are congruent. Option C states "Decide whether a sequence of transformations maps \( \triangle DEF \) to \( \triangle D'E'F' \)", which is the correct approach as a sequence of rigid transformations (which include reflections, translations, rotations) can be used to check congruence.

Answer:

C. Decide whether a sequence of transformations maps \( \triangle DEF \) to \( \triangle D'E'F' \)