# Similar Triangles

### Hannah Harris

## What Is Triangle Similarity Criterion ?

Triangle Similarity Criterion is known to be used when proving whether or not two of more triangles are similar. They are SSS (side side side), SAS (side angle side), and AA (angle angle).

## How Do You Use Triangle Similarity Criterion To Prove Triangles Similar ?

Here are some examples :

## Similar Triangles By SSS These triangles are similar by the criterion named SSS because all 3 sets of sides are proportional. | ## Similar Triangles By SAS These triangles are similar by the criterion named SAS because 2 sets of sides are proportional along with 1 congruent set of angles in between. | ## Similar Triangles By AA These triangles are similar by the criterion named AA because 2 sets of angles are congruent. |

## Similar Triangles By SSS

These triangles are similar by the criterion named SSS because all 3 sets of sides are proportional.

## Similar Triangles By SAS

These triangles are similar by the criterion named SAS because 2 sets of sides are proportional along with 1 congruent set of angles in between.

## Using Similarity Criterion To Prove Triangles Similar

SSS - Used to prove triangles similar when all sides are proportional

SAS - Used to prove triangles similar when 2 sets of sides are similar and 2 angles are congruent in between

AA - Used to prove triangles similar when 2 sets or all angles are congruent

Similar triangle example problems | Similarity | Geometry | Khan Academy

## Pythagorean Theorem

Pythagorean Theorem is used to find one missing side length of a triangle instead of using proportions.