**Leg Acute Angle Theorem :**

Leg Acute (LA) Angle Theorem is the theorem which can be used to prove the congruence of two right triangles.

**Explanation :**

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.

This principle is known as Leg-Acute Angle theorem.

Check whether two triangles PQR and RST are congruent.

**Solution :**

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

(ii) QR = RS (Given)

(iii) ∠PRQ = ∠SRT (Vertical Angles)

Hence, the two triangles PQR and RST are congruent by **Leg-Acute (LA) 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. 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, "Leg Acute Theorem".

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