can a translation and a reflection map $\triangle qrs$ to $\triangle tuv$? explain why or why not.\n$circ$…

can a translation and a reflection map $\triangle qrs$ to $\triangle tuv$? explain why or why not.\n$circ$ no, the triangles are not congruent.\n$circ$ yes, a translation mapping vertex q to vertex t and a reflection across the line containing $overline{qs}$ will map $\triangle qrs$ to $\triangle tuv$.\n$circ$ no, the triangles are obtuse.\n$circ$ yes, a translation mapping vertex s to vertex t and a reflection across the line containing $overline{rs}$ will map $\triangle qrs$ to $\triangle tuv$.

can a translation and a reflection map $\triangle qrs$ to $\triangle tuv$? explain why or why not.\n$circ$ no, the triangles are not congruent.\n$circ$ yes, a translation mapping vertex q to vertex t and a reflection across the line containing $overline{qs}$ will map $\triangle qrs$ to $\triangle tuv$.\n$circ$ no, the triangles are obtuse.\n$circ$ yes, a translation mapping vertex s to vertex t and a reflection across the line containing $overline{rs}$ will map $\triangle qrs$ to $\triangle tuv$.

Answer

Brief Explanations:

First, confirm the triangles are congruent: matching marks show corresponding sides/angles are equal, so $\triangle QRS \cong \triangle TUV$. Next, analyze the transformations: translating vertex $S$ to $T$ aligns a corresponding vertex, then reflecting across the line with $\overline{RS}$ maps the remaining congruent corresponding parts to match $\triangle TUV$. The other options are incorrect: the triangles are congruent, obtuse triangles can be mapped with these transformations, and translating $Q$ to $T$ does not align the corresponding parts correctly for the reflection step.

Answer:

Yes, a translation mapping vertex S to vertex T and a reflection across the line containing $\overline{RS}$ will map $\triangle QRS$ to $\triangle TUV$.