A.1 Similar Triangles

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Two triangles $T_1,T_2$ are similar when

(AAA — angle angle angle) The angles of $T_1$ are the same as the angles of $T_2\text{.}$
(SSS — side side side) The ratios of the side lengths are the same. That is
\begin{align*} \frac{A}{a} &= \frac{B}{b} = \frac{C}{c} \end{align*}
(SAS — side angle side) Two sides have lengths in the same ratio and the angle between them is the same. For example
\begin{align*} \frac{A}{a} &= \frac{C}{c} \text{ and angle $\beta$ is same} \end{align*}