Question

given: circle x with radius r and circle y with radius s. prove: circle x is similar to circle y. statements: translate x to y, circle x ~ circle y, dilate circle x by s/r, circle with center x has radius r, circle with center y has radius s. assemble the proof by dragging tiles to the statements and reasons columns.

Explanation:

Step1: Start with given information

Statement: circle with center X has radius r, circle with center Y has radius s. Reason: Given.

Step2: Translate one - circle to the other

Statement: translate X to Y. Reason: Translations preserve shape and size, and are rigid motions.

Step3: Dilate to make radii equal

Statement: dilate circle X by s/r. Reason: A dilation with scale factor k changes the size of a figure proportionally. After dilation, the radius of circle X will be r×(s/r)=s, which is the radius of circle Y. Since we can map circle X to circle Y using a translation and a dilation, the two circles are similar.

Answer:

Statements	Reasons
circle with center Y has radius s	Given
translate X to Y	Translations are rigid - motions
dilate circle X by s/r	Dilations create similar figures