# Does SAS work for similarity?

## Does SAS work for similarity?

SAS means side, angle, side, and refers to the fact that two sides and the included angle of a triangle are known. The SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

Can you use SAS for similar triangles?

You can prove that triangles are similar using the SAS~ (Side-Angle-Side) method. SAS~ states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are congruent.

What is SAS similarity?

The SAS similarity criterion states that If two sides of one triangle are respectively proportional to two corresponding sides of another, and if the included angles are equal, then the two triangles are similar.

### Why does SSA not like similarity?

Knowing only side-side-angle (SSA) does not work because the unknown side could be located in two different places. Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles. The same is true for side angle side, angle side angle and angle angle side.

How do you know if triangles are similar in SAS?

SAS (Side-Angle-Side) If two pairs of corresponding sides are in proportion, and the included angle of each pair is equal, then the two triangles they form are similar.

Does SAS prove congruence or similarity?

Putting all this together, we can see say that the triangles are similar by Side Angle Side (SAS). In a pair of similar triangles, all three corresponding angle pairs are congruent and corresponding side pairs are proportional.

## Is AAA a similarity theorem?

Euclidean geometry … may be reformulated as the AAA (angle-angle-angle) similarity theorem: two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.

Is there a SSA theorem?

An SSA congruence theorem does exist. sides and the corresponding nonincluded angle of the other, then the triangles are congruent. That is, the SSA condition guarantees con. gruence if the angles indicated by the A are right or obtuse.