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Section A.1 Similar Triangles

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*}