56.) Congruent Figures—figures that have the same size and shape 57.) Similar Figures—figures that have the same exact shape but different size (angles in similar figures are always congruent) A B C DF E ∆ABC ~ ∆DEF Similar Symbol ~ = ~ Congruent Symbol

58.) Corresponding Parts—the matching parts in congruent or similar figures (parts are always proportional in similar figures) A B C DF E AB ~ DE BC ~ EF AC ~ DF Sides Angles C = F B = E A = D

Are they congruent figures?

These figures are similar figures.

These figures are not similar.

Are they similar figures?

When two figures are similar, the ratios of the lengths of their corresponding sides are equal. Write a ratio comparing two sides of ∆ABC: AB AC Now write a ratio comparing two sides of ∆DEF that match with ∆ABC DE DF

AB DE AC DF Are these ratios equal? Use cross multiplication to check. = = 6 x 5 = 3 x = 30 YES!

If you know that two objects are similar, you can use proportions and cross multiplication to find the length of an unknown side. Let's find the length of side EF, labeled x. A B C D E F 4 x 3 AB DE BC EF = PROPORTION x = 9x = 15( 3) 9x = 45 x = 5 ∆ABC ∆DEF ~