Angle Angle Side Postulate

Proving Congruent Triangles with AAS

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

angle angle side picture

Identify Angle Angle Side relationship

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

Problem 1

Identify the coordinates of all complex numbers represented in the graph below.

Identify Angle Angle Side relationship (AAS)

Practice Proofs

Proof 1

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

loading AAS proof
Proof 2

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

loading AAS proof

Can you identify the error in the AAS proof below?

What is wrong with the proof below?

Identify Angle Angle Side relationship (AAS)

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

to FE and BE to be able to state that their is a pair of congruent sides in the two triangles.
back toTriangle Proof