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Question

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\\( \overline { p q } \\) is parallel to \\( \overline { r s } \\). \\( \overline { p r } \\) and \\( \overline { q s } \\) are perpendicular to \\( \overline { p q } \\) and \\( \overline { r s } \\).

the ratio of the lengths of \\( \overline { p r } \\) and \\( \overline { q s } \\) is \\( \square : \square \\).

Explanation:

Step1: Recall the property of parallel lines

If two lines \(PQ\parallel RS\) and \(PR\perp PQ\), \(QS\perp RS\), then \(PR\) and \(QS\) are the perpendicular distances between the parallel lines \(PQ\) and \(RS\).

Step2: Use the property of perpendicular distances between parallel lines

The perpendicular distance between two parallel lines is constant. So, \(PR = QS\).

Answer:

\(1:1\)