Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
\\(overline{pq}\\) is parallel to \\(overline{rs}\\). \\(overline{pr}\\) and \\(overline{qs}\\) are perpendicular to \\(overline{pq}\\) and \\(overline{rs}\\).
the ratio of the lengths of \\(overline{pr}\\) and \\(overline{qs}\\) is \\(square : square\\).

Explanation:

Step1: Identify the figure type

Since \( \overline{PQ} \parallel \overline{RS} \) and \( \overline{PR} \perp \overline{PQ} \), \( \overline{QS} \perp \overline{RS} \), the figure \( PQSR \) is a rectangle (or a parallelogram with right angles). In a rectangle (or such a parallelogram with perpendicular sides), the lengths of the sides perpendicular to the parallel sides (here \( \overline{PR} \) and \( \overline{QS} \)) are equal.

Step2: Determine the ratio

If two lengths are equal, their ratio is \( 1:1 \).

Answer:

\( 1 : 1 \)