In the previous chapter it was mentioned that a 3×5 photo could be
enlarged to fit on a billboard. In this case the images would be the same, but
one would be much bigger than the other. In math, we call that type of like-
ness similarity. When two figures, such as triangles, have the same propor-
tions between their respective angles and sides, but are different sizes, it is said
that they are similar triangles. Remember the four postulates that can be
used to prove that two triangles are congruent? Well there are three postu-
lates that are used to demonstrate that triangles are similar. Two of these pos-
tulates are based on the ratios and proportions of the sides of the triangles,
so before exploring them, we are going to discuss ratiosand proportions.
Ratios and Proportions: The Basics
A ratiois a comparison of any two quantities. If I have 10 bikes and you
have 20 cars, then the ratio of my bikes to your cars is 10 to 20. This ratio
is simplified to 1 to 2 by dividing each side of the ratio by the greatest com-
mon factor (in this case, 10). Ratios are commonly written with a colon
between the sets of objects being compared, but it is more useful in math-
ematical computations to write ratios as fractions. The ratio of bikes to