**4.5 Triangle Congruence: ASA, AAS, and HL**

**Definitions:**

Included Side- the common side of two consecutive angles in a polygon

Included Side

**Postulates/Theorems:**

Angle-Side-Angle (ASA) Congruence Postulate- If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent

Angle-Side-Angle (ASA) Congruence Postulate

**Angle-Angle-Side (AAS) Congruence Theorem**- If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent

**Hypotenuse-Leg (HL) Congruence Theorem**- If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent

*Note: If you have trouble remembering which are postulate and which are theorems look at the letter pattern. ASA, SSS and SAS are all postulates and the letters all have a symmetry about them. AAS and HL have no pattern and they are the theorems.

**Examples:**