Question

think about the process how can you decide if $\triangle def \cong \triangle def$? is $\triangle def \cong \triangle def$? explain.

how can you decide if $\triangle def \cong \triangle def$
a. decide whether a sequence of translations maps $\triangle def$ to $\triangle def$.
b. decide whether a sequence of rotations maps $\triangle def$ to $\triangle def$.
c. decide whether a sequence of rigid motions maps $\triangle def$ to $\triangle def$.
d. decide whether a sequence of reflections maps $\triangle def$ to $\triangle def$.

Explanation:

To determine if two triangles are congruent, we use the concept of rigid motions (translations, rotations, reflections). A rigid motion preserves the shape and size of a figure. So, we check if a sequence of rigid motions (which includes translations, rotations, and reflections) can map one triangle to the other. Option C says to decide if a sequence of rigid motions maps \( \triangle DEF \) to \( \triangle D'E'F' \), which is the correct approach as rigid motions preserve congruence.

Answer:

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