# SAS Similarity (Side-Angle-Side Similarity, SAS~)

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

## Theorem

If two corresponding sides of two triangles are proportional

and if the included angles of those two triangles are congruent,

then those two triangles are similar.

## Example

Draw the two triangles to prove its similarity:

△*APQ* and △*ABC*.

△*APQ* and △*ABC* have the same angle (red).

And *AQ*/*AC* = 2/5.

Then, to use the SAS similarity,*AP*/*AB* has to be 2/5.*AP*/*AB* = *AQ*/*AC* = 2/5.

So the answer is*C**AP*/*AB* = 2/5.