G.233 figures similar polygon — Heath

VI.21

Figures which are similar to the same rectilineal figure are also similar to one another.

For let each of the rectilineal figures A, B be similar to C;

I say that A is also similar to B.

For, since A is similar to C,
it is equiangular with it and has the sides about the equal angles proportional. [G.217]
A B C
Again, since B is similar to C,
it is equiangular with it and has the sides about the equal angles proportional.
Therefore each of the figures A, B is equiangular with C and with C has the sides about the equal angles proportional;
therefore A is similar to B.
Q. E. D.

Dependency Graph

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Required for

G.236, G.238, G.239, G.240, G.241, G.243, G.407, G.408, G.413, G.414, G.419, G.420, G.437, G.438, G.443, G.444, G.448, G.449, G.451, G.458, G.459, G.464, G.465, G.477, G.478, G.479, G.480, G.481, G.482, G.486, G.487, G.491, G.492, G.494, G.495, G.496, G.589, G.597, G.601