Congruent and Similar

Similar and Congruent Figures Congruent polygons have all sides congruent and all angles congruent. Similar polygons have the same shape; they may or may not have the same size.

Exercise Which of the following pairs are congruent and which are similar?

Examples These figures are similar and congruent. They’re the same shape and size. These figures are similar but not congruent. They’re the same shape, but not the same size.

Another Example These figures are neither similar nor congruent. They’re not the same shape or the same size. Even though they’re both triangles, they’re not similar because they’re not the same shape triangle. Note: Two figures can be similar but not congruent, but they can’t be congruent but not similar. Think about why!

Congruent Figures When 2 figures are congruent, i.e. 2 figures have the same shape and size,  Corresponding angles are equal  Corresponding sides are equal  Symbol : 

Congruent Triangles AB = XY, BC = YZ, CA = ZX  A =  X,  B =  Y,  C =  Z A C B X Z Y Note : Corresponding vertices are named in order.