Want to see correct answers?
Login or join for free!
Question Group Info

This question group is public and is used in 5 tests.

Author: nsharp1
No. Questions: 10
Created: Nov 29, 2018
Last Modified: 6 years ago

All Circles are Similar

View group questions.

To print this group, add it to a test.

Given two circles, one with center A (pictured below) and one with center B (not pictured), are they similar?

Circle with Center Point A
Grade 10 Circles CCSS: HSG-C.A.1
A.
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
C.
If we are to translate circle B to circle A, which of the following translations would accomplish this?
  1. Translate circle B by →AB.
  2. Translate circle B by →BA.
  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
E.
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
F.
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.
Grade 10 Circles CCSS: HSG-C.A.1
G.
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
H.
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
I.
Not only are all circles similar, but all spheres are similar as well. Are these two facts related? Why or why not?
  1. No, it is just chance.
  2. No, a circle is two dimensional and a sphere is three dimensional.
  3. Yes, the reason being that both for circles and spheres, their shape is always the same and their size depends on the radius.
  4. Yes, the reason being that both are not polygons.
Grade 10 Circles
J.
Given the work in steps B - H to show that two circles are similar, could we use this to show that any two spheres are similar? If so, what needs to be changed or added?
  1. No, this is not possible.
  2. Yes, by starting with spheres, and projecting them onto the xy-plane, we can then follow the steps already established.
  3. Yes, but we would need to perform completely different transformations since we are now working in three dimensions.
  4. Yes, start with spheres instead of circles and then follow nearly identical steps.