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\begin{document}

%-------------------------------------------------------------------

\section*{similarity}

\hypertarget{similarity}{}\section*{{Similarity}}\label{similarity}

Two shapes are \textbf{similar} if one can be obtained from the other by a series of rotations, reflections, translations, and scaling.

If two shapes are similar then the following hold:

\begin{itemize}%
\item Corresponding angles on the two shapes are equal.
\item There is a fixed scale factor such that corresponding lengths on the two shapes are related by multiplying by this scale factor.
\item The ratio of two lengths in one shape is the same as the ratio of the corresponding lengths in the other.

\end{itemize}
\hypertarget{similar_triangles}{}\subsection*{{Similar Triangles}}\label{similar_triangles}

When the two shapes are triangles then the following statements are equivalent:

\begin{itemize}%
\item The two triangles are similar
\item The angles in one triangle are the same as the angles in the other
\item The ratios of the lengths in one triangle are the same as in the other

\end{itemize}
[[!redirects similar triangle]] [[!redirects similar triangles]] [[!redirects similar shape]] [[!redirects similar shapes]] [[!redirects similar]] [[!redirects scale factor]]



\end{document}