Similar triangles

Triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are in proportion. That is, if triangle $ABC$ is similar to triangle $DEF$, then $\angle A = \angle D$, $\angle B = \angle E$, $\angle C = \angle F$, and $\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}$.

Important properties

• Corresponding angles of similar triangles are equal.

• Corresponding sides of similar triangles are in the same ratio (proportional).

• The ratio of perimeters of similar triangles is equal to the ratio of their corresponding sides.

• The ratio of areas of similar triangles is equal to the square of the ratio of their corresponding sides.