Question

given: \\( \overline { p r } \cong \overline { s u } \\), \\( \overline { p q } \cong \overline { s t } \\)
what additional information is needed to prove the triangles congruent by sss?
\\( \bigcirc \\) a. \\( \overline { q r } \cong \overline { t u } \\)
\\( \bigcirc \\) b. \\( \angle q \cong \angle t \\)
\\( \bigcirc \\) c. \\( \angle r \cong \angle u \\)
\\( \bigcirc \\) d. \\( \angle p \cong \angle s \\)

Explanation:

SSS congruence requires all three pairs of corresponding sides to be equal. Given $\overline{PR} \cong \overline{SU}$ and $\overline{PQ} \cong \overline{ST}$, the missing corresponding sides are $\overline{QR}$ and $\overline{TU}$. Proving these equal completes the SSS condition.

Answer:

a. $\overline{QR} \cong \overline{TU}$