There are 4 basic transformations for let's say, plane figures, for the moment. They are i) translation ie sliding a figure in a particular direction. ii) reflection ie reflecting a figure about a line or if you like a mirror image. iii) rotation ie rotating or spinning a figure around a point. iv) enlargement ie changing the size of a figure by scaling up or down, leaving the figures to be similar. Except for the last transformation all the others preserve the properties of the original figure ie the image is congruent to the original figure.
One way to prove all circles are similar is take any 2 general circles as in the diagram then translating one on to the other so that the centres of each are the same point ie translate A onto B. By the definition of a circle and a translation we have 2 concentric circles. Therefore as each point on a circumference is equidistant to the centre we can say that the larger circle is an enlargement of the smaller circle by a factor of s/r for all points.
'That's a description of how the proof might go...now it's a matter of putting it down more mathematically...which depends on what level you are at. Hope it helps you understand a bit better.
There are 4 basic transformations for let's say, plane figures, for the moment. They are i) translation ie sliding a figure in a particular direction. ii) reflection ie reflecting a figure about a line or if you like a mirror image. iii) rotation ie rotating or spinning a figure around a point. iv) enlargement ie changing the size of a figure by scaling up or down, leaving the figures to be similar. Except for the last transformation all the others preserve the properties of the original figure ie the image is congruent to the original figure.
One way to prove all circles are similar is take any 2 general circles as in the diagram then translating one on to the other so that the centres of each are the same point ie translate A onto B. By the definition of a circle and a translation we have 2 concentric circles. Therefore as each point on a circumference is equidistant to the centre we can say that the larger circle is an enlargement of the smaller circle by a factor of s/r for all points.
'That's a description of how the proof might go...now it's a matter of putting it down more mathematically...which depends on what level you are at. Hope it helps you understand a bit better.
