Answer: B
The correct second step for the given proof is;
[tex]\begin{gathered} \frac{C}{C^{\prime}}=\frac{2\pi r}{2\pi r^{\prime}} \\ and\text{;} \\ \frac{C}{C^{\prime}}=\frac{r}{r^{\prime}} \end{gathered}[/tex]by the division property of equality.
Explanation:
We want to find the correct second step for the given proof.
Recall that from division property of equality, when we have;
a=b and c=d, dividing the equations by each other, the equation will still be equal;
[tex]\frac{a}{c}=\frac{b}{d}[/tex]For the given Prove;
statement 1 states that the circumference circle 1 and 2 can be expressed as;
[tex]\begin{gathered} C=2\pi r \\ \text{and} \\ C^{\prime}=2\pi r^{\prime} \end{gathered}[/tex]So, for step 2;
Applying the division property of equality, we have;
[tex]\begin{gathered} \frac{C}{C^{\prime}}=\frac{2\pi r}{2\pi r^{\prime}} \\ \text{which then equals;} \\ \frac{C}{C^{\prime}}=\frac{r}{r^{\prime}} \end{gathered}[/tex]Therefore, the correct second step for the given proof is;
[tex]\begin{gathered} \frac{C}{C^{\prime}}=\frac{2\pi r}{2\pi r^{\prime}} \\ and\text{;} \\ \frac{C}{C^{\prime}}=\frac{r}{r^{\prime}} \end{gathered}[/tex]by the division property of equality.
