Question

the following figures show a translation. since translations are rigid motions, select all true statements. ∠b ≅ ∠i, overline{kn} ≅ overline{df}, ∠d ≅ ∠n, overline{af} ≅ overline{jn}, ∠a ≅ ∠k

Explanation:

Step1: Understand the property of translation

Translation is a rigid motion. Rigid motions (translations, rotations, reflections) preserve side - lengths and angle - measures. That is, if a figure is translated, the corresponding angles and corresponding sides of the original figure and the translated figure are congruent.

Step2: Analyze each statement

• For \(\angle B\cong\angle I\):

Since translation preserves angles, if \(\angle B\) and \(\angle I\) are corresponding angles (assuming the translation mapping), then \(\angle B\cong\angle I\) is True.

• For \(\overline{KN}\cong\overline{DF}\):

Translation preserves side - lengths. If \(\overline{KN}\) and \(\overline{DF}\) are corresponding sides (assuming the translation mapping), then \(\overline{KN}\cong\overline{DF}\) is True.

• For \(\angle D\cong\angle N\):

If we assume the translation mapping, \(\angle D\) and \(\angle N\) are not corresponding angles. So \(\angle D\cong\angle N\) is False.

• For \(\overline{AF}\cong\overline{JN}\):

If we assume the translation mapping, \(\overline{AF}\) and \(\overline{JN}\) are not corresponding sides. So \(\overline{AF}\cong\overline{JN}\) is False.

• For \(\angle A\cong\angle K\):

If we assume the translation mapping, \(\angle A\) and \(\angle K\) are not corresponding angles. So \(\angle A\cong\angle K\) is False.

Answer:

\(\angle B\cong\angle I\) and \(\overline{KN}\cong\overline{DF}\) are the True statements.