How do we prove two circles are similar what transformations are required to show circles are similar?

What transformations are required to show circles are similar?

To show that any two circles are similar you need to perform a translation and/or a dilation.

How can transformations be used to prove two figures are similar?

In general, similarity transformations preserve angles. Side lengths are enlarged or reduced according to the scale factor of the dilation. This means that similar figures will have corresponding angles that are the same measure and corresponding sides that are proportional.

Which method is valid for proving that two circles are similar?

Which method is valid for proving that two circles are similar? Calculate the ratio of radius to circumference for each circle and show that they are equal.

Which of the following explains why all circles are similar?

Which of the following explains why all circles are similar? … All circles have the same diameter, and therefore have the same shape.

How are similarity transformations and congruence transformations alike?

Similar figures have the same shape but not necessarily the same size. Congruence transformations preserve length and angle measure. When the scale factor of the dilation(s) is not equal to 1 or −1, similarity transformations preserve angle measure only.

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How do you know if two figures are similar?

Two figures are considered to be “similar figures” if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors. Equal scale factors mean that the lengths of their corresponding sides have a matching ratio.

Which statement is valid when a circumscribed circle of an obtuse triangle is constructed?

4. Which statement is valid when a circumscribed circle of an obtuse triangle is constructed? A. The longest side of the triangle lies on the diameter of the circle.

Are concentric circles similar?

Concentric circles: Concentric circles are simply circles that all have the same center. They fit inside each other and are the same distance apart all the way around. All concentric circles are similar to each other.

Why do we use similarity transformation?

The use of similarity transformations aims at reducing the complexity of the problem of evaluating the eigenvalues of a matrix. Indeed, if a given matrix could be transformed into a similar matrix in diagonal or triangular form, the computation of the eigenvalues would be immediate.