Angle-Angle-Side or AAS Congruence Postulate is a rule which can be used to prove the congruence of two triangles.

**Explanation :**

If two angles and non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

**Example : **

**In the diagram given below, prove that ΔEFG ≅ ΔJHG using two column proof.**

**Solution :**

FE ≅ JH ∠E ≅ ∠J ∠EGF ≅ ∠JGH ΔEFG ≅ ΔJHG |
Given Given Vertical Angles Theorem AAS Congruence Postulate |

**1. Side-Side-Side (SSS) Congruence Postulate**

If three sides of one triangle is congruent to three sides of another triangle, then the two triangles are congruent.

**2. Side-Angle-Side (SAS) Congruence Postulate**

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

**3. Angle-Side-Angle (ASA) Congruence Postulate**

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

**4. Hypotenuse-Leg (HL) Theorem**

If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.

**5. Leg-Acute (LA) Angle Theorem**

If a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the two right triangles are congruent.

**6. Hypotenuse-Acute (HA) Angle Theorem**

If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.

**7. Leg-Leg (LL) Theorem**

If the legs of one right triangle are congruent to the legs of another right triangle, then the two right triangles are congruent.

**Caution :**

**SSA** and **AAA** can not be used to test congruent triangles.

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