which statements can be concluded from the diagram and used to prove that the triangles are similar by the…

which statements can be concluded from the diagram and used to prove that the triangles are similar by the sas similarity theorem?\no $\frac{rs}{vu}=\frac{st}{ut}$ and $angle scongangle u$\no $\frac{rs}{vu}=\frac{st}{ut}=\frac{rt}{vt}$\no $\frac{rs}{vu}=\frac{tu}{ts}$ and $angle scongangle u$\no $\frac{rs}{vu}=\frac{tu}{ts}=\frac{rt}{vt}$

which statements can be concluded from the diagram and used to prove that the triangles are similar by the sas similarity theorem?\no $\frac{rs}{vu}=\frac{st}{ut}$ and $angle scongangle u$\no $\frac{rs}{vu}=\frac{st}{ut}=\frac{rt}{vt}$\no $\frac{rs}{vu}=\frac{tu}{ts}$ and $angle scongangle u$\no $\frac{rs}{vu}=\frac{tu}{ts}=\frac{rt}{vt}$

Answer

Explanation:

Step1: Record lados y ángulos

Tenemos en triángulos $\triangle RST$ y $\triangle VUT$, $RS = 12$, $ST=16$, $VU = 8$, $UT = 6$, $\angle S=\angle U = 90^{\circ}$.

Step2: Aplicar SAS

La Teorema de Similitud SAS establece que si los lados correspondientes de dos triángulos están en proporción y los ángulos incluidos son congruentes, entonces los triángulos son similares. Calculamos las proporciones de los lados: $\frac{RS}{VU}=\frac{12}{8}=\frac{3}{2}$ y $\frac{ST}{UT}=\frac{16}{6}=\frac{8}{3}$. Pero si consideramos $\frac{RS}{VU}=\frac{ST}{UT}$ y $\angle S=\angle U$, se cumple SAS.

Answer:

$\frac{RS}{VU}=\frac{ST}{UT}$ y $\angle S=\angle U$ (primera opción)