The Angle Angle Side postulate (often abbreviated as AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included angle of another triangle, then these two triangles are congruent.

**Example** of Angle Angle Side Proof (AAS)

$$ \triangle $$ABC $$ \triangle $$XYZ

- Two angles and a non-included side are congruent
- $$ \angle A \cong \angle X $$(angle)
- $$ \angle C \cong \angle Z $$(angle)
- AB $$\cong$$ XY (side)

- Therefore, by the Angle Angle Side postulate (AAS), the triangles are congruent.

### Identify Angle Angle Side relationship

Identify which pair of triangles below does **NOT** illustrate an angle angle side (AAS) relationship.

**Practice** Proofs

##### Proof 1

Prove that $$ \triangle ABC \cong \triangle DEC $$

##### Proof 2

Prove that $$ \triangle ABC \cong \triangle DEF $$

#### Can you identify the error in the AAS proof below?

The error involves the side needed to prove two triangles congruent by the Angle Angle Side Postulate

FE and BC are **NOT **full sides in either triangle. You would need to use the additon property of equality to add segment BE