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 { a b } \\) and \\( \overline { d c } \\), and \\( \overline { e f } \\) and \\( \overline { h g } \\).
complete the statements.
\\( \overline { a b } \\) and \\( \overline { d c } \\) are?
\\( \overline { e f } \\) and \\( \overline { h g } \\) are?
the transformation maps parallel sides onto? sides.

Explanation:

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

By observing the figure \(ABCD\), we can see that \(\overline{AB}\) and \(\overline{DC}\) are parallel.

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

Since figure \(EFGH\) is the translation of figure \(ABCD\), and translation preserves the parallel - property of line segments. So \(\overline{EF}\) and \(\overline{HG}\) are parallel.

Step3: Analyze the property of translation for parallel sides

Translation is a rigid transformation. In a translation, if two sides are parallel in the original figure, their images (the corresponding sides in the translated figure) are also parallel. So 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.