Side-Side-Side or SSS 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 = √[(x _{2} - x_{1})^{2} + **

**Here (**x_{1}, y_{1}) = B(-7, 0) and (x_{2}, y_{2}) = C(-4, 5)

**BC = √[(-4 + 7)² + (5 - 0)²]**

**BC = √[3² + 5²]**

**BC = √[9 + 25]**

**BC = √34**

**Length of GH : **

**GH = ****√[(x _{2} - x_{1})^{2} + **

**Here (**x_{1}, y_{1}) = G(1, 2) and (x_{2}, y_{2}) = H(6, 5)

**GH = √[(6 - 1) ^{2} + (5 - 2)^{2}]**

**GH = √[5 ^{2} + 3^{2}]**

**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.

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