Question

if \\(\overline{ps} \cong \overline{rs}\\) and \\(pq = 46\\), what is \\(qr\\)?
image of a geometric figure with points r, s, p, q, where s is the midpoint of rp, qs is perpendicular to rp, forming two right triangles qsr and qsp
\\(qr = \square\\)
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Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since \(\overline{PS}\cong\overline{RS}\), \(\angle PSQ=\angle RSQ = 90^{\circ}\), and \(\overline{SQ}\cong\overline{SQ}\) (common side), by the HL Congruence Theorem, \(\triangle PQS\cong\triangle RQS\).

Step2: Use the property of congruent triangles

If \(\triangle PQS\cong\triangle RQS\), then their corresponding sides are equal. So, \(PQ = QR\).

Answer:

\(46\)