SSS Criterion for Congruence of Triangles

The triangles are congruent when the lengths of three sides of one triangle are equal to the lengths of corresponding sides of the other triangle. It is called Side-Side-Side (SSS) criterion for the congruence of triangles.

Introduction

There are three sides in every triangle. The congruence of any two triangles can be determined by comparing the lengths of corresponding sides of them.

If length of every side of one triangle is equal to the length of corresponding side of other triangle, then the two triangles are congruent geometrically and they are called the congruent triangles.

In this case, comparison of corresponding three sides of triangles is a criteria for determining the congruence of triangles. Hence, it is called side-side-side criterion but it is simply called SSS criterion for congruence of triangles.

Now, let’s study the SSS (Side-Side-Side) criterion in detail from an understandable example.

Example

$\Delta ABC$ and $\Delta LMN$ are two triangles but their lengths are unknown. However, the length of side of every triangle can be measured by a ruler.

It is measured that

In $\Delta ABC$, $AB \,=\, 5\,cm$, $BC \,=\, 7\,cm$ and $CA \,=\, 6\,cm$

In $\Delta LMN$, $LM \,=\, 5\,cm$, $MN \,=\, 7\,cm$ and $NL \,=\, 6\,cm$

Compare the lengths of corresponding sides.

$(1).\,\,\,$ $AB \,=\, LM \,=\, 5\,cm$

$(2).\,\,\,$ $BC \,=\, MN \,=\, 7\,cm$

$(3).\,\,\,$ $CA \,=\, NL \,=\, 6\,cm$

The lengths of three sides of $\Delta ABC$ are equal to the lengths of corresponding sides of $\Delta LMN$. Therefore, the two triangles are called congruent triangle.

$\therefore \,\,\,\,\,\,$ $\Delta ABC \,\cong\, \Delta LMN$

In this example, the three corresponding sides of both triangles are considered as a criteria for determining the congruence of triangles. Hence, the criteria is called SSS (Side-Side-Side) criterion in geometry.