Question

given △trs≅△vxw, which of the following corresponding pairs is correct? (1 point)
○ st≅wv
○ ∠t≅∠w
○ rs≅vx
○ tr≅xw

Explanation:

Step1: Recall congruent - triangle properties

When $\triangle TRS\cong\triangle VXW$, the order of the vertices gives the corresponding parts. That is, $T$ corresponds to $V$, $R$ corresponds to $X$, and $S$ corresponds to $W$.

Step2: Analyze each option

• For $\overline{ST}\cong\overline{WV}$, the order of endpoints is wrong. The correct correspondence should be $\overline{ST}\cong\overline{WV}$ if the vertices are in the right - order of congruence. Here, $S$ corresponds to $W$ and $T$ corresponds to $V$.
• For $\angle T\cong\angle W$, the correct corresponding angle of $\angle T$ is $\angle V$ since $T$ corresponds to $V$ in $\triangle TRS\cong\triangle VXW$.
• For $\overline{RS}\cong\overline{VX}$, since $R$ corresponds to $X$ and $S$ corresponds to $W$, this is incorrect. The correct side - correspondence for $\overline{RS}$ is $\overline{XW}$.
• For $\overline{TR}\cong\overline{XV}$, since $T$ corresponds to $V$ and $R$ corresponds to $X$, the correct corresponding sides are $\overline{TR}\cong\overline{VX}$ and $\overline{TR}\cong\overline{XV}$ is correct as the order of naming a line - segment does not matter for congruence.

Answer:

$\overline{TR}\cong\overline{XV}$