Question

which statement describes why △abc and △def are congruent by sas? when △abc is translated 2 units left and 1 unit down, $overline{ab}$ maps to $overline{de}$, $overline{bc}$ maps to $overline{ef}$, and ∠b maps to ∠e. when △abc is translated 6 units left, $overline{ab}$ maps to $overline{de}$, $overline{bc}$ maps to $overline{ef}$, and ∠b maps to ∠e. when △abc is translated 6 units left, $overline{ab}$ maps to $overline{de}$, $overline{bc}$ maps to $overline{ef}$, and ∠f maps to ∠c. when △abc is translated 2 units left and 1 unit down, $overline{ab}$ maps to $overline{de}$, $overline{bc}$ maps to $overline{ef}$, and ∠f maps to ∠c.

Explanation:

Step1: Recall SAS congruence criterion

Two triangles are congruent by SAS (Side - Angle - Side) if two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of the other triangle.

Step2: Analyze the translation

We need to find the translation that maps two sides and the included - angle of $\triangle ABC$ to the corresponding parts of $\triangle DEF$.
Looking at the coordinates of the vertices of the triangles on the graph, we can see that when $\triangle ABC$ is translated 6 units left, $\overline{AB}$ maps to $\overline{DE}$, $\overline{BC}$ maps to $\overline{EF}$, and $\angle B$ maps to $\angle E$.

Answer:

When $\triangle ABC$ is translated 6 units left, $\overline{AB}$ maps to $\overline{DE}$, $\overline{BC}$ maps to $\overline{EF}$, and $\angle B$ maps to $\angle E$.