Two triangles are similar triangles if there is a composition of transformations that maps one triangle onto the other. In other words, two triangles are similar if they have the same shape and the ratios of their corresponding linear measures are equal. To algebraically denote that two triangles are similar, the symbol ~ is used. When writing a similarity statement, the corresponding vertices must be listed in the same order. For the triangles above, two possible similarity statements are given.

In the applet below, move the slider to apply a composition of similarity transformations to the triangle. The resulting triangle is then a similar triangle. To determine whether two triangles are similar according to the given information, three triangle similarity theorems can be used.