Question

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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 first pair of line segments

In the given figure, \(\overline{AB}\) and \(\overline{DC}\) are parallel. This can be observed as they have the same slope (horizontal - like in the grid, moving from left - to - right without rising or falling in a non - parallel way).

Step2: Analyze the second pair of line segments

\(\overline{EF}\) and \(\overline{HG}\) are also parallel. They follow the same direction and will never intersect, which is the property of parallel lines.

Step3: Analyze the transformation property

Since the first pair (\(\overline{AB}\) and \(\overline{DC}\)) are parallel and the second pair (\(\overline{EF}\) and \(\overline{HG}\)) are parallel, and considering the nature of the transformation (translation in this case, as the shape is just moved across the grid), 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.