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) Responses 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 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 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 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 .

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To prove that any two circles are similar, the key is to recognize that similarity involves a transformation that maps one figure onto another while preserving shape.

Given that circles A and B have different radii (a ≠ b), Amias can use the concept of dilation. The appropriate step would be to dilate circle A by a factor of \(\frac{b}{a}\). This will scale the radius of circle A so that it matches the radius of circle B:

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.

This option directly addresses the necessary transformation for similarity, which is a dilation, indicating that the shapes remain proportional and hence similar regardless of the size.

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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) Responses 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 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 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 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 .

1 answer

To prove that any two circles are similar, the key is to recognize that similarity involves a transformation that maps one figure onto another while preserving shape.

Given that circles A and B have different radii (a ≠ b), Amias can use the concept of dilation. The appropriate step would be to dilate circle A by a factor of \(\frac{b}{a}\). This will scale the radius of circle A so that it matches the radius of circle B:

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.

This option directly addresses the necessary transformation for similarity, which is a dilation, indicating that the shapes remain proportional and hence similar regardless of the size.

GPT-4o mini · Answer

To prove that any two circles are similar, the key is to recognize that similarity involves a transformation that maps one figure onto another while preserving shape.

Given that circles A and B have different radii (a ≠ b), Amias can use the concept of dilation. The appropriate step would be to dilate circle A by a factor of \(\frac{b}{a}\). This will scale the radius of circle A so that it matches the radius of circle B:

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.

This option directly addresses the necessary transformation for similarity, which is a dilation, indicating that the shapes remain proportional and hence similar regardless of the size.