Question

termine if $\triangle abc \cong \triangle def$. if they are congruent, determine which postulate proves they are congruent.
$\triangle abc$ is not congruent to $\triangle def$.
$\triangle abc \cong \triangle def$ using side - side - side triangle congruence postulate
$\triangle abc \cong \triangle def$ using side - angle - side triangle congruence postulate
$\triangle abc \cong \triangle def$ using angle - side - angle triangle congruence postulate

Explanation:

Step1: Identify given congruent parts

In △ABC and △DEF: ∠A = ∠D = 120°, side adjacent to ∠A (let’s say AB) ≅ side adjacent to ∠D (DE), side opposite to ∠A’s adjacent side (AC) ≅ side opposite to ∠D’s adjacent side (DF) (marked with equal signs/crosses).

Step2: Match with congruence postulate

The pattern is two sides and the included angle congruent, which is the Side-Angle-Side (SAS) postulate. Thus, △ABC ≅ △DEF by SAS.

Answer:

△ABC ≅ △DEF using Side-Angle-Side triangle congruence postulate