Question

(a) find the length of each segment. give an exact answer (not a decimal approximation).

pq = sqrt{61}

rs = sqrt{65}

tv = sqrt{61}

(b) check all statements that are true below.

□ overline{pq} cong overline{rs}

□ overline{pq} cong overline{tv}

□ overline{rs} cong overline{tv}

□ none of these are true

Explanation:

Segments are congruent if their lengths are equal. We know \(PQ = \sqrt{61}\), \(RS=\sqrt{65}\), and \(TV = \sqrt{61}\).

• For \(\overline{PQ}\cong\overline{RS}\): Since \(\sqrt{61}

eq\sqrt{65}\), this statement is false.

• For \(\overline{PQ}\cong\overline{TV}\): Since \(\sqrt{61}=\sqrt{61}\), this statement is true.
• For \(\overline{RS}\cong\overline{TV}\): Since \(\sqrt{65}

eq\sqrt{61}\), this statement is false.

Answer:

\(\overline{PQ}\cong\overline{TV}\)