**ANGLE SIDE ANGLE Congruence Postulate (ASA) :**

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

**Explanation :**

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.

**Example 1 :**

In the diagram given below, prove that ΔABD ≅ ΔEBC using two column proof.

**Solution :**

BD ≅ BC AD || EC ∠D ≅ ∠C ∠ABD ≅ ∠EBC ΔABD ≅ ΔEBC |
Given Given Alternate Interior Angles Theorem Vertical Angles Theorem ASA Congruence Postulate |

**Example 2 :**

Check whether two triangles PQR and CDE are congruent.

**Solution :**

(i) ∠R = ∠D (Given)

(ii) PR = ED (Given)

(iii) ∠P = ∠E (Given)

Hence, the two triangles PQR and CDE are congruent by **ASA** 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-Angle-Side (AAS) Congruence Postulate**

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.

**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.

Apart from the problems given above, if you need more problems on triangle congruence postulates,

After having gone through the stuff given above, we hope that the students would have understood, "Angle Side Angle congruence postulate".

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