We all know that triangles are polygons having three sides.
Two or more triangles are said to be congruent to each other when all the corresponding sides and corresponding angles match with each other.
Congruence of triangles:
Two triangles are congruent 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.
What are the parts of two congruent triangles?
Let us consider the figure of two congruent triangles given below.
From the figure given above, it is understood that \(\triangle ABC\) and \(\triangle DEF\) look similar but only differ in position.
Since they are congruent to each other, it is a given that all the corresponding sides and corresponding angles are equal.
Now let us try to find the corresponding vertices, corresponding sides, and corresponding angles of these two triangles.
Corresponding vertices: \(A\) and \(D\), \(B\) and \(E\), and \(C\) and \(F\)
Corresponding sides: \(AB\) and \(DE\), \(BC\) and \(EF\), and \(CA\) and \(FD\)
Corresponding angles: \(∠A\) and \(∠D\), \(∠B\) and \(∠E\), and \(∠C\) and \(∠F\)
Congruence of triangles not only depends on the measure of sides and angles but also depends on the matching of vertices.
Considering every detail thus discussed, the two triangles \(ABC\) and \(DEF\) have six possible correspondences. They are: