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 \( \overline{PR}, \overline{QS} \perp \overline{PQ}, \overline{RS} \), the figure \( PQSR \) is a rectangle (or a right - angled trapezoid with both non - parallel sides perpendicular, which is a rectangle).

Step2: Recall properties of rectangles (or right - angled trapezoids with perpendicular non - parallel sides)

In a rectangle, the lengths of the two sides that are perpendicular to the parallel sides (the heights) are equal. In this case, \( \overline{PR} \) and \( \overline{QS} \) are the sides perpendicular to the parallel sides \( \overline{PQ} \) and \( \overline{RS} \). So the length of \( \overline{PR} \) is equal to the length of \( \overline{QS} \).

Step3: Determine the ratio

If \( PR = QS \), then the ratio \( \frac{PR}{QS}=\frac{1}{1} \), so the ratio of the lengths of \( \overline{PR} \) and \( \overline{QS} \) is \( 1:1 \).

Answer:

1 : 1