Question

tu || sv. find rv. u v r 6 3 s 6 t rv = save answer

Explanation:

Step1: Identify similar triangles

Since $TU \parallel SV$, $\triangle RSV \sim \triangle RTU$ by AA similarity.

Step2: Set up proportion of sides

Corresponding sides are proportional:
$$\frac{RV}{RU} = \frac{RS}{RT}$$
Let $RV = x$. Then $RU = x + 6$, $RS = 3$, $RT = 6$.
$$\frac{x}{x+6} = \frac{3}{6}$$

Step3: Simplify and solve for x

Simplify $\frac{3}{6}$ to $\frac{1}{2}$:
$$\frac{x}{x+6} = \frac{1}{2}$$
Cross-multiply:
$$2x = x + 6$$
Subtract $x$ from both sides:
$$2x - x = 6$$
$$x = 6$$

Answer:

$6$