Hypotenuse Acute Angle or HA Theorem is the theorem which can be used to prove the congruence of two right triangles.

**Explanation :**

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.

This principle is known as Hypotenuse-Acute Angle theorem.

**Example 1 :**

Check whether two triangles PQR and ABC are congruent.

**Solution :**

(i) PQ = BC (Hypotenuse)

(ii) ∠Q = ∠B (Acute angle)

Hence, the two triangles PQR and ABC are congruent by **Hypotenuse-Acute (HA) Angle** theorem.

**Example 2 :**

Check whether two triangles OPQ and IJK are congruent.

**Solution :**

(i) Triangle OPQ and triangle IJK are right triangles. Because they both have a right angle.

(ii) OQ = JK (Hypotenuse)

(iii) ∠Q = ∠J (Given)

Hence, the two triangles OPQ and IJK are congruent by **Hypotenuse-Acute (HA) Angle **theorem.

**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. 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.

**5. 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.

**6. 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.

**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.

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