unit 5 - similar triangles

proportion

an equation of two equal ratios

property of proportions

the product of the means is the product of the extremes

you can reciprocate each ratio in a proportion

a/b \= c/d then b/a \= d/c

you can switch the means and/or the extremes

a/b \= c/d then a/c \= b/d OR d/b \= c/a OR d/c \= b/a

means

the middle terms of a proportion

extremes

the first and last terms of a proportion

similarity

two shapes are similar if their corresponding angles are congruent and the corresponding sides are proportional (equal ratios)

(- ratio is the scale factor)

if two shapes are similar, the ratio of their perimeters is the same as their scale factor

angle-angle similarity postulate

if two angles of one triangle are congruent to two angles of another, then the two triangles are similar