**SIDE SIDE SIDE Congruence Postulate (SSS) :**

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

**Explanation :**

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

**Example 1 :**

In the diagram given below, prove that ΔPQW ≅ ΔTSW.

**Solution :**

PQ ≅ ST PW ≅ TW QW ≅ SW ΔPQW ≅ ΔTSW |
Given Given Given SSS Congruence Postulate |

**Example 2 :**

In the diagram given below, prove that ΔABC ≅ ΔFGH.

**Solution :**

Because AB = 5 in triangle ABC and FG = 5 in triangle FGH,

AB ≅ FG.

Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,

AC ≅ FH.

Use the distance formula to find the lengths of BC and GH.

**Length of BC : **

**BC = √[(x₂ - x₁)² + (y₂ - y₁)²]**

**Here (**x₁, y₁) = B(-7, 0) and (x₂, y₂) = C(-4, 5)

**BC = √[(-4 + 7)² + (5 - 0)²]**

**BC = √[3² + 5²]**

**BC = √[9 + 25]**

**BC = √34**

**Length of GH : **

**GH = √[(x₂ - x₁)² + (y₂ - y₁)²]**

**Here (**x₁, y₁) = G(1, 2) and (x₂, y₂) = H(6, 5)

**GH = √[(6 - 1)² + (5 - 2)²]**

**GH = √[5² + 3²]**

**GH = √[25 + 9]**

**GH = √34**

**Conclusion :**

Because BC = √34 and GH = √34,

BC ≅ GH

All the three pairs of corresponding sides are congruent. By SSS congruence postulate,

ΔABC ≅ ΔFGH

**1. 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 tw o triangles are congruent.

**2. 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.

**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, "Side side side congruence postulate".

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