# How are ratio and proportion used in geometry?

May 15, 2015

Polygons are "similar" is the ratios of their sides are proportional.

We see this kind of thing when we zoom in or out. When we expand of shrink.
And when we work with scale drawings or maps.

If a scale drawing has one side of a triangle is 1 in and another is 3 in, and the scale is 1 in = 1 ft, then in the built priject, one side will be 1 ft and the other 3 ft. The ratio is still 1 to 3.

Is we zoom in (or blow up) a rectangle with length 4 and width 3, then any larges version will have proportional sides.
So if we make the length 10, then we can find the width by solving the proportion:

$\frac{4}{3} = \frac{10}{w}$

$4 w = 30$

$w = \frac{30}{4} = \frac{15}{2} = 7 \frac{1}{2}$

One more example:

In a 30-60-90 triangle if we make the hypotenuse length $2$, then the short leg (the one opposite the ${30}^{\circ}$ angle) has length $1$

In any 30-60-90 triangle, the ratio of the hypotenuse and the short leg is the same. It is proportional.