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Common Core Standard HSG-C.A.1 Questions

Prove that all circles are similar.

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Grade 10 Circles CCSS: HSG-C.A.1

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If the two circles' radii are congruent, can the circles still be shown to be similar?
  1. No, since they are congruent.
  2. No, since there exists no scale factor that will dilate one circle onto the other.
  3. Yes, since all congruent shapes are similar (with scale factor 1).
  4. Yes, since congruent radii means they have the same area, and any shapes with equal areas are similar.
Grade 10 Circles CCSS: HSG-C.A.1

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Is the work and are conclusions from parts B through G enough to prove that any two circles are similar? If not, why?
  1. Yes, they are enough.
  2. No, we need to consider the case where we move circle A instead of circle B.
  3. No, we need set up a two-column table.
  4. No, we need to consider more sizes of circles first.
Grade 10 Circles CCSS: HSG-C.A.1

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Which of the following is the best definition for similar figures?
  1. Figures which are similar in area and perimeter.
  2. Figures having congruent sides and angles.
  3. One shape can be mapped to another through a sequence of rotations, translations, reflections, and/or dilation.
  4. One shape can be mapped to another through rigid transformations.
Grade 10 Circles CCSS: HSG-C.A.1

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If we are to translate circle B to circle A, which of the following translations would accomplish this?
  1. Translate circle B by [math]vec{AB}[/math].
  2. Translate circle B by [math]vec{BA}[/math].
  3. Translate circle B by its radius.
  4. Translate circle B by the radius of circle A.
Grade 10 Circles CCSS: HSG-C.A.1

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After increasing the radius of circle B, such that it is equal to the radius of circle A, how can we be sure that the two circles will lie exactly on top of each other?
  1. Since a circle is defined as a set of points a certain distance from a center, all the points on circle B will now be the same distance away from A as the points on circle A.
  2. Because a dilation is a rigid transformation, all the points on circle B must move by the same amount.
  3. Since the centers of the two circles are coincident, the rest of the circle must also be coincident.
  4. We can't be sure and need to use more radii from each circle to show this.
Grade 10 Circles CCSS: HSG-C.A.1

This question is a part of a group with common instructions. View group »

If circle B's radius is larger that circle A's radius, what must change in our work to show that the two circles are similar?
  1. Nothing needs to change.
  2. They cannot be similar in this case.
  3. Circle A must be translated to circle B.
  4. The dilation scale factor must change.

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