Question

the figure that results from a transformation is called the image. figure abcd is translated to get its image, figure efgh.
look at \\(\overline{ab}\\) and \\(\overline{dc}\\), and \\(\overline{ef}\\) and \\(\overline{hg}\\).
complete the statements.
\\(\overline{ab}\\) and \\(\overline{dc}\\) are ? .
\\(\overline{ef}\\) and \\(\overline{hg}\\) are ? .
the transformation maps parallel sides onto ? sides.

Explanation:

Step1: Analyze \( \overline{AB} \) and \( \overline{DC} \)

In the original figure \( ABCD \), \( \overline{AB} \) and \( \overline{DC} \) are horizontal sides (from the grid). Since they are horizontal, they have the same slope (0), so they are parallel.

Step2: Analyze \( \overline{EF} \) and \( \overline{HG} \)

In the image figure \( EFGH \), \( \overline{EF} \) and \( \overline{HG} \) are also horizontal sides (from the grid). They have the same slope (0), so they are parallel.

Step3: Analyze the transformation

Translation is a rigid transformation that preserves the shape and orientation. So, parallel sides in the original figure are mapped to parallel sides in the image. Thus, the transformation maps parallel sides onto parallel sides.

Answer:

\( \overline{AB} \) and \( \overline{DC} \) are parallel.
\( \overline{EF} \) and \( \overline{HG} \) are parallel.
The transformation maps parallel sides onto parallel sides.

(For the blanks: first blank "parallel", second blank "parallel", third blank "parallel")