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

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

How to solve SSS similarity problems: theorem, example, and its solution.

Theorem

If three corresponding sides of two triangles are proportional, then those two triangles are similar.

If three corresponding sides of two triangles are proportional,
then those two triangles are similar.

Example

If AB/DE = AC/DF = 2, which of the following would be sufficient to prove that triangle ABC ~ triangle DEF?

Two corresponding sides of △ABC and △DEF are proportional:
AB/DE = AC/DF = 2.

And the followings are the ratios of the sides.

So find the following
that shows the missing proportionality:
BC/EF = 2.

If the followings are the congruences of angles,
then you should find the congruence of inscribed angles.

SAS similarity (Side-Angle-Side similarity)