Congruence of Triangle

Congruence means that one figure will exactly superimpose the other figure. Two congruent line segments have the same length and conversely two lines segments of equal length are congruent. or we can say that two line segments are congruent if and only if their lengths are equal. Similarly two angles are congruent if and only if their measures are equal, or we can say that two angles BAC and EDF are congruent if m

Two triangles are congruent if and only if one of them can be made to superpose on the other, so as to cover it exactly. Let be two congruent triangles. Then, we can superpose on , so as to cover it exactly. In such a superposition the vertices of will fall on the vertices of , in some order. Let us assume that the vertex A falls on vertex D, vertex B on vertex E and vertex C on vertex F.

Then, side AB falls on DE, BC on EF and CA on FD. Also superposes on the corresponding angle and  . Thus, the order in which the vertices match, automatically determines a correspondence between the sides and angles of the two triangles. And, if the superposition is exact i.e. the triangles are congruent, the corresponding sides and angles are congruent. Consequently, we get six equalities three of the corresponding sides and three of the corresponding angles. If superposes on exactly such that the vertices of fall on the vertices of in the following order

Then, we have the following six qualities         (i.e., corresponding sides are congruent)         (i.e., corresponding angles are congruent)

Congruence Relation

From the definition of congruence of two triangles, we obtain the following results:

(i) Every triangle is congruent to itself i.e.,

(ii) If , then

(iii) If , and , then

Note: It is important to write the correspondence  of vertices correctly for writing of congruence of triangles in symbolic form because but and the symbolic form is used to write corresponding parts of congruent triangles {C.P.C.T.}