### Theory:

Congruence of a triangle(polygon with three sides) is one of the types of congruence of a polygon.

Congruence of a triangle: Two triangles are congruence if their corresponding sides are equal in length and corresponding angles are equal in measure. That is if the two triangles are superimposed on each other, their sides and angles will coincide.

$\mathrm{\Delta}$ABC and $\mathrm{\Delta}$DEF have the same size and shape. They are congruent. This can be expressed as $\mathrm{\Delta}$ABC$\cong $$\mathrm{\Delta}$DEF.

That is, if we superimpose \(A\) on \(D\), \(B\) on \(E\) and \(C\) on \(F\), they cover each other exactly.

Thus, we have

Important!

**\(A\) and \(D\), \(B\) and \(E\), and \(C\) and \(F\).**

**Corresponding vertices:**** **

**\(AB\) and \(DE\), \(BC\) and \(EF\), and \(CA\) and \(FD\).**

**Corresponding sides:**** **

**\(∠A\) and \(∠D\), \(∠B\) and \(∠E\), and \(∠C\) and \(∠F\).**

**Corresponding angles:**

Congruence of triangles not just depend on the measure of sides and angles but also depends on the matching of vertices.

Consider two triangles $\mathrm{\Delta}$\(ABC\) and $\mathrm{\Delta}$\(DEF\). There is six possible correspondence. They are:

\(ABC\) $\leftrightarrow $ \(DEF\)

\(ABC\) $\leftrightarrow $ \(DFE\)

\(ABC\) $\leftrightarrow $ \(EDF\)

\(ABC\) $\leftrightarrow $ \(EFD\)

\(ABC\) $\leftrightarrow $ \(FDE\)

\(ABC\) $\leftrightarrow $ \(FED\).