Question

1. triangle abc was translated to create triangle edk using the transformation,

$(x,y)\
ightarrow(x - 9,y - 2)$.
which of the following congruence statements does not accurately describe the two
triangles?

Explanation:

When a figure is translated, the corresponding sides and angles are congruent. Let's check each option:

• For $\overline{KE}\cong\overline{CA}$: Since translation preserves length, if $K$ corresponds to $C$ and $E$ corresponds to $A$, then $\overline{KE}\cong\overline{CA}$.
• For $\angle KDE\cong\angle CBA$: Translation preserves angle measure. If $\angle KDE$ and $\angle CBA$ are corresponding angles, then they are congruent.
• For $\overline{BA}\cong\overline{DE}$: In a translation, the order of correspondence matters. If $\triangle ABC$ is translated to $\triangle EDK$, then $\overline{BA}$ corresponds to $\overline{DK}$ (not $\overline{DE}$).
• For $\angle DKE\cong\angle ABC$: Translation preserves angle measure. If $\angle DKE$ and $\angle ABC$ are corresponding angles, then they are congruent.

Answer:

$\overline{BA}\cong\overline{DE}$ (the option that does not accurately describe the congruence of the two triangles)