Question

George is given two circles, circle O and circle X, as shown. If he wants toprove that the two circles are similar, what would be the correct second stepin his proof?Given: The radius of circle O is r, and the radius of circle X is .Prove: Circle Ois similar to circle X.1.C = 2rr and C'= 2rr' by the definition of circumference.2._3. d= 2rand d = 2r by the definition of diameter.d= 2r4. d'= 2r andby the division property of equality.5d=2rby the substitution property.and6. Circle Ois similar to circle Xbecause all the linear dimensions are in thesame proportion.

Answer 1

Answer: B

The correct second step for the given proof is;

`\begin{gathered} (C)/(C^(\prime))=(2\pi r)/(2\pi r^(\prime)) \\ and\text{;} \\ (C)/(C^(\prime))=(r)/(r^(\prime)) \end{gathered}`

by the division property of equality.

Step-by-step 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;

`(a)/(c)=(b)/(d)`

For the given Prove;

statement 1 states that the circumference circle 1 and 2 can be expressed as;

`\begin{gathered} C=2\pi r \\ \text{and} \\ C^(\prime)=2\pi r^(\prime) \end{gathered}`

So, for step 2;

Applying the division property of equality, we have;

`\begin{gathered} (C)/(C^(\prime))=(2\pi r)/(2\pi r^(\prime)) \\ \text{which then equals;} \\ (C)/(C^(\prime))=(r)/(r^(\prime)) \end{gathered}`

Therefore, the correct second step for the given proof is;

`\begin{gathered} (C)/(C^(\prime))=(2\pi r)/(2\pi r^(\prime)) \\ and\text{;} \\ (C)/(C^(\prime))=(r)/(r^(\prime)) \end{gathered}`

by the division property of equality.