formulate an argument to prove that all squares and circles are similar

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Expert Solution

A circle is the set of points equidistant from a given point. Consequently, a circle is defined by only the radius.

Proof: • Move the center of the smaller circle onto the center of the larger circle. Translate circle B, by vector , onto circle A. The circles are now concentric (they have the same center). • A dilation is needed to increase the size of circle B to coincide with circle A. A value that when multiplied by r₁ will create r₂ is needed. The scale factor, x, to increase circle B:
• A translation, followed by a dilation with scale factor will map one circle onto the other, thus proving that the circles are similar. • We found the similarity transformations! Similarly we can prove the same for the square also . :)

milcah answered 1 year ago

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