Question

determine if $\triangle abc \cong \triangle def$. if they are congruent, determine which postulate proves they are congruent.
options:

• $\triangle abc$ 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 congruent parts

In $\triangle ABC$ and $\triangle DEF$, we see that two sides are marked congruent (the tick marks) and the included angle (the $120^\circ$ angle) between those sides is congruent.

Step2: Recall congruence postulates

The Side - Angle - Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Here, the two sides with tick marks and the included $120^\circ$ angle satisfy SAS. So $\triangle ABC\cong\triangle DEF$ by SAS.

Answer:

$\triangle ABC \cong \triangle DEF$ using Side - Angle - Side triangle congruence postulate (the option: $\triangle ABC \cong \triangle DEF$ using Side - Angle - Side triangle congruence postulate)