Congruent triangles have the same shape and the same size: every pair of corresponding sides and angles is equal. The order of the letters tells you which parts correspond. Triangle $ABC$ congruent to triangle $DEF$ means $A$ matches $D$, $B$ matches $E$ and $C$ matches $F$, so $AB = DE$, $BC = EF$ and $AC = DF$.

These are enough to prove two triangles congruent: three pairs of equal sides (SSS); two sides and the angle between them (SAS); two angles and the side between them (ASA); two angles and a side not between them (AAS). Two other combinations are not enough: three equal angles (AAA) only guarantee the same shape, and two sides with an angle that is not between them (SSA) don't always fix the triangle.

Similar triangles have the same shape but can differ in size. Corresponding angles are equal, and every pair of corresponding sides has the same ratio, the scale factor. Two pairs of equal angles are enough to prove similarity (AA), because the third angles must then match too. Match sides by letter order, just as for congruence, and multiply, never add: a similar triangle's sides are a multiple of the original's, not a fixed amount longer.

A segment parallel to one side of a triangle cuts off a smaller triangle similar to the whole one. In the figure below, $DE \parallel BC$, so angle $ADE$ equals angle $ABC$ (corresponding angles) and angle $A$ is shared. Triangle $ADE$ is similar to triangle $ABC$, and $\frac{AD}{AB} = \frac{AE}{AC} = \frac{DE}{BC}$. Compare $AD$ with the whole side $AB$, not with the piece $DB$.

If every side of a triangle is multiplied by $k$, its perimeter is multiplied by $k$ and its area by $k^2$. A triangle whose sides are twice as long has 4 times the area.