## Why does SSA congruence not work?

## Why does SSA congruence not work?

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.

### What is AAA congruence criterion?

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.

#### What are the three similarity theorems?

These three theorems, known as Angle – Angle (AA), Side – Angle – Side (SAS), and Side – Side – Side (SSS), are foolproof methods for determining similarity in triangles.

**What is aa SSS SAS?**

AA-similarity. if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. SSS-similarity. if three sides of one triangle are proportional to three corresponding sides of another triangle, then the triangles are similar. SAS-similarity.

**Is AAA a similarity criterion?**

In two Triangles,if corresponding angles are equal , then their corresponding sides are in the same ratio , i.e they are proportional and hence the two triangles are similar.

## Is AAA a similarity theorem?

### What is AAA criterion theorem?

If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar. We can prove this theorem by taking two triangles ABC and DEF.

#### What is AAA triangle congruence?

AAA means we are given all three angles of a triangle, but no sides. This is not enough information to decide if two triangles are congruent!

**Does SSA prove congruence?**

The SSA condition (Side-Side-Angle: two sides and a non-included angle being congruent) is, in general, not sufficient to prove congruence of triangles; in some cases you can in fact prove that the triangles are not congruent by making a counterexample, and in other cases additional data can make the proof possible.

**Is SSA a conguent theorem or postulate?**

SSA is not a postulate and you can find a video, More on why SSA is not a postulate: This IS the video.This video proves why it is not to be a postulate. Nonetheless, SSA is side-side-angles which cannot be used to prove two triangles to be congruent alone but is possible with additional information.

## What is SSA congruence rule?

ASA Congruence Rule: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent (ASA Congruence Rule).

### Which congruence theorem can be used to prove?

Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent. An included angle is an angle formed by two given sides.