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

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.

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

If the given triangles are similar, find the value of x.

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.