Question

select the correct answer from each drop - down menu.
in this figure, \\( \overline { a b } \\) and \\( \overline { c d } \\) are parallel.
\\( \overline { a b } \\) is perpendicular to line segment if the length of \\( \overline { e f } \\) is a units, then the length of \\( \overline { g h } \\) is units.

Explanation:

Step1: Recall the property of parallel lines and perpendicular segments

When two lines ($\overline{AB}$ and $\overline{CD}$) are parallel, and there are two perpendicular segments ($\overline{EF}$ and $\overline{GH}$) between them, the lengths of these perpendicular segments are equal. This is because the distance between two parallel lines is constant.

Step2: Apply the property to find the length of $\overline{GH}$

Since $\overline{AB}\parallel\overline{CD}$, and $\overline{EF}\perp\overline{AB}$ (as $\overline{EF}\perp\overline{CD}$ and $\overline{AB}\parallel\overline{CD}$), $\overline{GH}\perp\overline{AB}$ (as $\overline{GH}\perp\overline{CD}$ and $\overline{AB}\parallel\overline{CD}$). The length of $\overline{EF}$ is given as $a$ units. By the property of the distance between parallel lines (perpendicular segments between parallel lines are equal in length), the length of $\overline{GH}$ is also $a$ units. And $\overline{AB}$ is perpendicular to $\overline{EF}$ (because $\overline{EF}\perp\overline{CD}$ and $\overline{AB}\parallel\overline{CD}$).

Answer:

The first drop - down: $EF$ (assuming the options in the first drop - down are mis - labeled in the problem statement, as based on the figure and parallel line - perpendicular segment property, $\overline{AB}$ is perpendicular to $\overline{EF}$). The second drop - down: $a$ units.