Question

is △abc ≅ △def? if so, name the congruence postulate that applies.
given
\overline{ab} ≅ \overline{de}
\overline{bc} ≅ \overline{ef}
\overline{ca} ≅ \overline{fd}
a. congruent - asa
b. congruent - sas
c. might not be congruent
d. congruent - sss

Explanation:

Step1: Identify given congruent sides

We are given \( \overline{AB} \cong \overline{DE} \), \( \overline{BC} \cong \overline{EF} \), and \( \overline{CA} \cong \overline{FD} \).

Step2: Recall congruence postulates

The SSS (Side - Side - Side) congruence postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Here, all three corresponding sides of \( \triangle ABC \) and \( \triangle DEF \) are congruent. So by SSS postulate, \( \triangle ABC \cong \triangle DEF \).

Answer:

D. Congruent - SSS