Congruence of Triangles
Two figures are called congruent figures, when they have same shape and same size.
The relation between two figures being congruent is called congruence.
Two plane figures are congruent to each other if trace copy of one of the figures covers the other figure completely.
Two line segments are congruent, if they are of the same (or equal) length.
If two angles have the same measure, they are congruent. Also, if two angles are congruent, their measures are same.
Two triangles are congruent if they are exact copies of each other and when superposed, they cover each other exactly. In congruent triangles, the sides and angles which coincide by superposition are called corresponding sides and corresponding angles.
Criteria for congruency of triangles are:
SSS congruence rule: If under a given correspondence, the three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are said to be congruent by SSS rule of congruency.
SAS congruence rule: If under a given correspondence, two sides and angle included between them of a triangle are equal to two corresponding sides and the angle included between them of the another triangle, then the triangles are congruent.
ASA congruence rule: If under a given correspondence, two angles and the included side of a triangle are equal to two corresponding angles and included side of another triangle, then the triangles are congruent.
RHS congruence rule: Two right triangles are congruent, if the hypotenuse and one side of one triangle, are respectively equal to the hypotenuse and one side of the other triangle.