Refresher - Similar Triangles

Definition: Triangles are similar if they have the same shape, but can be different sizes. (They are still similar even if one is rotated, or one is a mirror image of the other). Triangles are similar if they have the same shape, but not necessarily the same size. You can think of it as "zooming in" or out making the triangle bigger or smaller, but keeping its basic shape.

Formally speaking, two triangles ${\displaystyle \Delta ABC}$ and ${\displaystyle \Delta DEF}$ are said to be similar if either of the following equivalent conditions holds:

1. Corresponding sides have lengths in the same ratio:
   i.e. ${\displaystyle \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}}$. This is equivalent to saying that one triangle is an enlargement of the other.
2. ${\displaystyle \angle BAC}$ is equal in measure to ${\displaystyle \angle EDF}$, and ${\displaystyle \angle ABC}$ is equal in measure to ${\displaystyle \angle DEF}$. This also implies that ${\displaystyle \angle ACB}$ is equal in measure to ${\displaystyle \angle DFE}$.
   
   In formal notation we can write
   
              ${\displaystyle \Delta ABC~\Delta DEF}$
   
   which is read as "Triangle ABC is similar to triangle DEF ".