Question

question 6 of 10
if $\triangle pqr \cong \triangle stu$, which statement must be true?
a. $\overline{pq} \cong \overline{su}$
b. $\angle p \cong \angle r$
c. $\overline{pq} \cong \overline{st}$
d. $\angle p \cong \angle t$

Explanation:

When two triangles are congruent ($\triangle PQR \cong \triangle STU$), their corresponding sides and angles are congruent. The order of the letters in the triangle names gives the correspondence: $P$ corresponds to $S$, $Q$ corresponds to $T$, and $R$ corresponds to $U$. So, side $\overline{PQ}$ (between $P$ and $Q$) corresponds to side $\overline{ST}$ (between $S$ and $T$), meaning $\overline{PQ} \cong \overline{ST}$.

• Option A: $\overline{PQ}$ should correspond to $\overline{ST}$, not $\overline{SU}$, so A is false.
• Option B: $\angle P$ corresponds to $\angle S$, not $\angle R$, so B is false.
• Option D: $\angle P$ corresponds to $\angle S$, not $\angle T$, so D is false.

Answer:

C. $\overline{PQ} \cong \overline{ST}$