Question

look at \\(\overline{ab}\\) and \\(\overline{dc}\\), and \\(\overline{ef}\\) and \\(\overline{hg}\\). complete the statements. \\(\overline{ab}\\) and \\(\overline{dc}\\) are perpendicular. \\(\overline{ef}\\) and \\(\overline{hg}\\) are perpendicular. the transformation maps parallel sides onto parallel sides.

Explanation:

Step1: Analyze $\overline{AB}$ and $\overline{DC}$

$\overline{AB}$ and $\overline{DC}$ are horizontal (or same - slope) line segments. In a coordinate grid, horizontal line segments have the same $y$ - coordinate change (0) for any $x$ - coordinate change, so their slopes are equal (slope $m=\frac{\Delta y}{\Delta x}$, here $\Delta y = 0$). Equal - slope lines are parallel, not perpendicular. So $\overline{AB}$ and $\overline{DC}$ are parallel.

Step2: Analyze $\overline{EF}$ and $\overline{HG}$

$\overline{EF}$ and $\overline{HG}$ are also horizontal line segments. Similar to $\overline{AB}$ and $\overline{DC}$, they have the same slope (slope = 0), so they are parallel, not perpendicular.

Step3: Analyze the transformation

The figure shows a translation (or a rigid transformation) of the left trapezoid - like figure to the right. Rigid transformations (translations, rotations, reflections) preserve the parallelism of lines. 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.