Similarity of Circles
Read this topicExplanations 4
- Similarity is a quality of scaling: two shapes are similar if you can scale one to be like the other, like these triangles ABC and DEF. Since all circles are of the same shape (…
By Anonymous
- If two shapes are similar to each other, they have the same shape, but not necessarily the same size. Consider the two circles below. While they have different colors and differ…
By Elise Molinaro
- In geometry, similarity is a property of at least two shapes relative to each other. If two shapes are similar, then they maintain the same properties in proportion to one anoth…
By Liza Sulkin
- Here's a great video detailing a proof that all circles are similar!
By Liza Sulkin
Problems 22
- If two circles have the same radius, which of the following is true?
- If the ratio between two circles' areas is 4:1, which of the following is true?
- Suppose you have two circles in different positions on the coordinate plane. Which of the following could be used to prove that the two circles are similar?
- Circle A has center at the origin and radius x. It is rotated 90∘90^{\circ}90∘ clockwise. Circle B has center at the origin and radius y. It is rotated 90∘90^{\circ}90∘ counterc…
- Circle A has center at (4, 4) and radius 9. Circle B has center at (4, 4) and radius 5. Circle C has center at (4, 4) and radius π\piπ. Which (if any) of these circles are similar?
- Any two circles are always:
- Ellipse X has a semi-major axis of length a and eccentricity 0. Ellipse Y has a semi-major axis of length b and eccentricity 0. Ellipse Z has a semi-major axis of length c and e…
- What is a circle defined by?
- Consider a circle with a scale factor of 3 with respect to the one above. What is it's radius?
- Consider the skeleton of a car wheel pictured above. Determine the scale factor of the circle shown by the center cap →\rightarrow→ the circle shown by the tire.
- Which of the following equations represents the scale factor needed to either decrease or increase the size of a circle?
- What is the scale factor needed to go from Pizza A to Pizza B?
- Which of the following are similar in this picture?
- If a dartboard has nnn concentric circles, how many similar circles are in one board?
- Suppose circle A has radius X and circle B has radius Y. When are these two circles similar?
- Suppose circle A has radius X and circle B has radius Y. When are these two circles congruent?
- Similar polygons are those with proportional corresponding sides. What analogous proportional structures do similar circles have?
- Fill in the blank: If two circles have proportional ________ , then they are similar.
- Congruent polygons are those with congruent corresponding sides. What analogous congruent structures do congruent circles have?
- In the slice, which layers of the Earth are similar circles?
- Consider spheres. In some sense, spheres can be considered 3D circles because they are the set of points that a constant distance away from a point in space. Suppose Sphere A ha…
- Every year, trees grow outward, and this can be visualized by the rings in their cross-sections. Every new ring (see above) represents another outer layer of the tree; thus, the…