# SSS Similarity (Side-Side-Side Similarity, SSS~)

How to use the SSS similarity theorem to solve similar triangles: theorem, example, and its solution.

## Theorem

For two triangles,

if three sides of each triangle are proportional,

then those two triangles are similar.

This is the SSS similarity theorem.

The ratios of each side, *k*, is called

the [scale factor] or the [constant of proportionality].

## Example

To compare the corresponding sides easily,

redraw the right triangle like this.

It says these two triangles are similar.

So write [ ~ ] between the triangles.

The sides of similar triangles are proportional.

So 2/4 = 4/8 = *x*/6.

2/4 = 4/8 = 1/2

So write the scale factor, 1/2,

next to the proportion.

So 2/4 = 4/8 = *x*/6 = 1/2.

Proportion

Solve the proportion *x*/6 = 1/2.

Multiply 6 to both sides.

Then *x* is equal to, 6/2, 3.