To prove that all circles are similar, you would use the sequence of similarity translations and dilation.
We can prove that all circles are similar by:
- Getting two circles
- Label the 2 circles. I.e. circle X and circle Y
- Now move the center of the circle X unto the center of the circle Y, this will give two circles with the same center, i.e. two concentric circles.
- Now you should Perform a dilation on one of the circles (i.e. resizing), till the circle overlap. Regardless of the size of the circles, they will always overlap, which then confirms the similarity, which implies they are similar.
<h2>Further Explanation</h2>
A similarity transformation refers to one or multiple rigid transformations (reflection, rotation, reflection) which is then followed by dilation. In a case a given figure is transformed by a similarity transformation, an image that is similar to the original figure is created.
A circle is the set of points that have the same distance from a specific point called the center. It can also be defined as a plane curve that consists of all points that have the same distance or equidistant from a given point. In a circle, the radius is the common distance of a given point on the curve from the center.
Parts of a circle include:
- The radius
- The circumference
- An arc
- The cord
- A semi-circle
- A tangent
- The diameter
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KEYWORDS:
- circles
- similar
- prove
- sequence of similarity
- cord
- perimeter
