Amias is trying to prove that any two given circles are similar. He starts by drawing circle A with a radius of a and circle B with a radius of b where a≠b . He then translates circle A so that circle A and circle B have the same center. How can he complete his proof to show that circle A is similar to circle B ?(1 point)

Question

Responses

Amias can rotate both circle A and circle B around their center points until they coincide. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.
Amias can rotate both circle upper A and circle upper B around their center points until they coincide. Because a sequence of transformations maps circle upper A onto circle upper B , circle upper A is similar to circle upper B .

Amias can dilate circle A by a factor of ab and show that the circles now coincide. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.
Amias can dilate circle upper A by a factor of Start Fraction a over b End Fraction and show that the circles now coincide. Because a sequence of transformations maps circle upper A onto circle upper B , circle upper A is similar to circle upper B .

Amias can rotate circle A around its center point until it coincides with circle B. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.
Amias can rotate circle upper A around its center point until it coincides with circle upper B . Because a sequence of transformations maps circle upper A onto circle upper B , circle upper A is similar to circle upper B .

Amias can dilate circle A by a factor of ba and show that the circles now coincide. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.
Amias can dilate circle upper A by a factor of Start Fraction b over a End Fraction and show that the circles now coincide. Because a sequence of transformations maps circle upper A onto circle upper B , circle upper A is similar to circle upper B .

Answer 1

To prove that two circles are similar, we need to consider the fact that similarity in geometry means that one figure can be transformed into another using a combination of rotations, translations, reflections, and dilations.

In the context of the options provided, the most appropriate way to demonstrate the similarity of circles A and B, where \( a \neq b \), involves dilation. Specifically, since circle A has radius \( a \) and circle B has radius \( b \), Amias can perform the following steps:

Amias can dilate circle A by a factor of \( \frac{b}{a} \) to show that the circles now coincide. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.

This choice correctly uses the concept of dilation with the appropriate scaling factor to demonstrate the similarity of the two circles. Thus, the correct response is:

Amias can dilate circle A by a factor of \( \frac{b}{a} \) and show that the circles now coincide. Because a sequence of transformations maps circle A onto circle B, circle A is similar to circle B.